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<units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="38" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="18" left="6" top="8.25" width="244.5" height="12" align-x="20.25" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Solving a system of equations using a "solve block"</inlineAttr> </f> </text> </region> <region region-id="22" left="24" top="32.25" width="171.75" height="60" align-x="39" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#000">example: solve the system of equations</c> <c val="#000"> <sp count="14"/>x + y + z = 10</c> <c val="#000"> <sp count="14"/>x - 2y = 5</c> <c val="#000"> <sp count="14"/>y - z = 6</c> <sp count="3"/> </text> </region> <region region-id="25" left="6" top="104.25" width="237" height="24" align-x="18" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <inlineAttr font-weight="normal"> <c val="#000080">1.<sp count="2"/>Guess the values of the unknowns</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="5"/>(use the < </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">: ></c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> key to assign values to the variables)</c> </inlineAttr> </text> </region> <region region-id="6" left="78" top="141" width="23.25" height="12.75" align-x="88.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="7" left="144" top="141" width="24.75" height="12.75" align-x="156" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="8" left="216" top="141" width="23.25" height="12.75" align-x="226.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">z</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="24" left="6" top="182.25" width="415.5" height="36" align-x="11.25" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080">2. Begin the solve block with the command <given>.<sp count="2"/>Next, type </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">n </c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080">equations in </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">n</c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080"> unknowns.<sp count="3"/>The equals signs must be typed as <</c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#000080">ctrl =>.<sp count="2"/>End the solve block with the command <find>.<sp count="2"/>The equals sign in the find command is the normal one.</c> </inlineAttr> </f> </text> </region> <region region-id="31" left="78" top="243" width="24" height="12.75" align-x="89.25" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="4"/> </region> <region region-id="3" left="96" top="273" width="58.5" height="12.75" align-x="138" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>10</ml:real> </ml:apply> </math> <rendering item-idref="5"/> </region> <region region-id="4" left="96" top="309" width="45.75" height="12.75" align-x="129.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:real>5</ml:real> </ml:apply> </math> <rendering item-idref="6"/> </region> <region region-id="26" left="96" top="345" width="38.25" height="12.75" align-x="122.25" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>6</ml:real> </ml:apply> </math> <rendering item-idref="7"/> </region> <region region-id="36" left="78" top="381" width="48.75" height="12.75" align-x="96" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> </math> <rendering item-idref="8"/> </region> <region region-id="38" left="6" top="428.25" width="415.5" height="36" align-x="11.25" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <c val="#000080">To carry out the calculation, click on the word "find" in the above expression and press the equal</c> <c val="#000080">< = > key.<sp count="2"/> </c> <c val="#000080">The answer is </c> <c val="#000080">x = 10.5, y = 2.75, z = -3.25</c> </text> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAB8AAAARCAYAAAAlpHdJAAAAAXNSR0IArs4c6QAAAARnQU1B AACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACVSURBVEhL7ZLdDYAwCIQ7FwMxD9Ow DMMgoIlWS5r40774JY22jdwdUnQiv/gUhosLgRbkeB8qHsKlzBF3GslFCcyRuUJmRXsCyXpV sd5t394iabsXBiUxI9Srvpu9rI6z/J8LKYSBbf8BuTibuCVqt/zI28k9dRx64e/S5wPnh9F6 T4E2BWceDhxj1aG67YP5xSegugACebpEuRi8mQAAAABJRU5ErkJggg==</item> <item item-id="2">iVBORw0KGgoAAAANSUhEUgAAACEAAAARCAYAAABTnsXCAAAAAXNSR0IArs4c6QAAAARnQU1B AACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACnSURBVEhL7ZIBCoAgDEU9lwfaeXYa L7PDrG1pWKwMwwrqgZAY8+27wC/glyh8W4IwcoBk349ImEAIz0ooThKJQc1sgewEQo71fsX8 f67Rhf8c+dK6MCEwUt64EGMs8pvVMNydCTuIKKUV6fZKqw12JUpnetZOQRmQhJFgLrIkMoZj 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Mathcad Professional 14.0 <description/> <author>laptop</author> <company/> <keywords/> <revisedBy>laptop</revisedBy> </userData> <identityInfo> <revision>1</revision> <documentID>FC5E87B5-5803-42C1-8BA3-31ADB4A0C9BF</documentID> <versionID>C4577A17-E6B2-4790-9F27-C8E46C00895E</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> 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fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="38" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="18" left="6" top="8.25" width="244.5" height="12" align-x="20.25" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false">Solving a system of equations using a "solve block"</inlineAttr> </f> </text> </region> <region region-id="22" left="24" top="32.25" width="171.75" height="60" align-x="39" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <c val="#000">example: solve the system of equations</c> <c val="#000"> <sp count="14"/>x + y + z = 10</c> <c val="#000"> <sp count="14"/>x - 2y = 5</c> <c val="#000"> <sp count="14"/>y - z = 6</c> <sp count="3"/> </text> </region> <region region-id="25" left="6" top="104.25" width="237" height="24" align-x="18" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <inlineAttr font-weight="normal"> <c val="#000080">1.<sp count="2"/>Guess the values of the unknowns</c> </inlineAttr> <inlineAttr font-weight="normal"> <c val="#000080"> <sp count="5"/>(use the < </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">: ></c> </inlineAttr> </f> <inlineAttr font-weight="normal"> <c val="#000080"> key to assign values to the variables)</c> </inlineAttr> </text> </region> <region region-id="6" left="78" top="141" width="23.25" height="12.75" align-x="88.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="1"/> </region> <region region-id="7" left="144" top="141" width="24.75" height="12.75" align-x="156" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="8" left="216" top="141" width="23.25" height="12.75" align-x="226.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">z</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="24" left="6" top="182.25" width="415.5" height="36" align-x="11.25" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080">2. Begin the solve block with the command <given>.<sp count="2"/>Next, type </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">n </c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080">equations in </c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false"> <c val="#000080">n</c> </inlineAttr> </f> <inlineAttr font-weight="normal" font-style="normal"> <c val="#000080"> unknowns.<sp count="3"/>The equals signs must be typed as <</c> </inlineAttr> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <c val="#000080">ctrl =>.<sp count="2"/>End the solve block with the command <find>.<sp count="2"/>The equals sign in the find command is the normal one.</c> </inlineAttr> </f> </text> </region> <region region-id="31" left="78" top="243" width="24" height="12.75" align-x="89.25" align-y="252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">Given</ml:id> </math> <rendering item-idref="4"/> </region> <region region-id="3" left="96" top="273" width="58.5" height="12.75" align-x="138" align-y="282" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> </ml:apply> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>10</ml:real> </ml:apply> </math> <rendering item-idref="5"/> </region> <region region-id="4" left="96" top="309" width="45.75" height="12.75" align-x="129.75" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> <ml:real>5</ml:real> </ml:apply> </math> <rendering item-idref="6"/> </region> <region region-id="26" left="96" top="345" width="38.25" height="12.75" align-x="122.25" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:equal/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:apply> <ml:real>6</ml:real> </ml:apply> </math> <rendering item-idref="7"/> </region> <region region-id="36" left="78" top="381" width="48.75" height="12.75" align-x="96" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:apply xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:Find auto-method="true" method="linear" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:sequence> </ml:apply> </math> <rendering item-idref="8"/> </region> <region region-id="38" left="6" top="428.25" width="415.5" height="36" align-x="11.25" align-y="438" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <c val="#000080">To carry out the calculation, click on the word "find" in the above expression and press the equal</c> <c val="#000080">< = > key.<sp count="2"/> </c> <c val="#000080">The answer is </c> <c val="#000080">x = 10.5, y = 2.75, z = -3.25</c> </text> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAB8AAAARCAYAAAAlpHdJAAAAAXNSR0IArs4c6QAAAARnQU1B AACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACVSURBVEhL7ZLdDYAwCIQ7FwMxD9Ow DMMgoIlWS5r40774JY22jdwdUnQiv/gUhosLgRbkeB8qHsKlzBF3GslFCcyRuUJmRXsCyXpV sd5t394iabsXBiUxI9Srvpu9rI6z/J8LKYSBbf8BuTibuCVqt/zI28k9dRx64e/S5wPnh9F6 T4E2BWceDhxj1aG67YP5xSegugACebpEuRi8mQAAAABJRU5ErkJggg==</item> <item item-id="2">iVBORw0KGgoAAAANSUhEUgAAACEAAAARCAYAAABTnsXCAAAAAXNSR0IArs4c6QAAAARnQU1B AACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAACnSURBVEhL7ZIBCoAgDEU9lwfaeXYa L7PDrG1pWKwMwwrqgZAY8+27wC/glyh8W4IwcoBk349ImEAIz0ooThKJQc1sgewEQo71fsX8 f67Rhf8c+dK6MCEwUt64EGMs8pvVMNydCTuIKKUV6fZKqw12JUpnetZOQRmQhJFgLrIkMoZj 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