Question 50521
Graph each pair of equations in the same coordinate plane. 
3x+2y=0 [Rewrite in y=mx+b formate by solving for y]
3x-3x+2y=-3x [Solve for y]
2y=-3x
2y/2=-3/2x
y=-3/2x + 0  Graph with a slope of (-3/2) and a y-intercept of (0, 0)
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x-2y=8 [Rewrite in y=mx+b formate by solving for y]
x-x-2y=-x+8
-2y=-x+8
-2y/-2=-x/-2+8/-2
y=1/2x-4 [Graph with a slope of (1/2) and a y-intercept of (0, -4)

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Graphing:

{{{ graph( 300, 200, -6, 5, -6, 10, (-3/2)x+0, (1/2)x-4) }}}


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Find the coordinates of the point where the graphs intersect. 
Looking at the graph, the two lines intersect or cross at points (2, -3).
Plug (2, -4) into each original equation to prove that these are the common points.
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Then show by substitution that the coordinates satisfy both equations. 
3x+2y=0 [Plug-in points (2, -3)
3(2)+2(-3)=0 [Solve]
6-6=0
0=0 [Proved that (2, -3) are points of this line]

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x-2y=8  [Plug-in points (2, -3)
(2)-2(-3)=8
2+6=8
8=8 {Proved that (2, -3 ) are points of this line also]