Solve Linear Systems by Graphing



3OLVE ,INEAR 3YSTEMS BY 'RAPHING 'OAL

9OUR .OTES

+ 'RAPH AND SOLVE SYSTEMS OF LINEAR EQUATIONS

6/#!"5,!29 3YSTEMS OF LINEAR EQUATIONS
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3OLUTION OF A SYSTEM OF LINEAR EQUATIONS
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#ONSISTENT INDEPENDENT SYSTEM
ʏˆ˜i>ÀÊÃÞÃÌi“Ê̅>ÌÊ …>ÃÊiÝ>V̏Þʜ˜iÊ܏Ṏœ˜

3/,6).' ! ,).%!2 3934%- 53).' 4(% '2!0( !.$ #(%#+ -%4(/$ 3TEP  Ê À>«…Ê BOTH EQUATIONS IN THE SAME COORDINATE PLANE &OR EASE OF GRAPHING YOU MAY WANT TO WRITE EACH EQUATION IN Ê Ãœ«i‡ˆ˜ÌiÀVi«ÌÊvœÀ“Ê  3TEP  %STIMATE THE COORDINATES OF THE Ê «œˆ˜ÌʜvÊ ˆ˜ÌiÀÃiV̈œ˜Ê  3TEP  Ê …iVŽÊ THE COORDINATES ALGEBRAICALLY BY SUBSTITUTING INTO EACH EQUATION OF THE ORIGINAL LINEAR SYSTEM



,ESSON  s !LGEBRA  .OTETAKING 'UIDE

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9OUR .OTES

5SE THE GRAPH AND CHECK METHOD

%XAMPLE 

3OLVE THE LINEAR SYSTEM X  Y   XY

%QUATION  %QUATION 

3OLUTION  Ê À>«…Ê BOTH EQUATIONS 4O EASE GRAPHING WRITE EACH EQUATION IN SLOPE INTERCEPT FORM

 









  


















 %STIMATE THE POINT OF INTERSECTION 4HE TWO LINES APPEAR TO INTERSECT AT Ê ÓÊ Ê ÎÊ   #HECK WHETHER Ê ÓÊ Ê ÎÊ IS A SOLUTION BY SUBSTITUTING Ê ÓÊ FOR X AND Ê ÎÊ FOR Y IN EACH OF THE ORIGINAL EQUATIONS %QUATION 

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"ECAUSE Ê ÓÊ Ê ÎÊ IS A SOLUTION OF EACH EQUATION IN THE LINEAR SYSTEM IT IS A Ê ÃœṎœ˜ÊœvÊ̅iʏˆ˜i>ÀÊÃÞÃÌi“

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,ESSON  s !LGEBRA  .OTETAKING 'UIDE



9OUR .OTES

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