How do you solve $x-y=-2$ , $2x+y=6$ by graphing?

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Answer 1 · 2017-04-28T04:09:21

Solution is $(4/3,10/3)$

To solve such linear equations we should draw the graphs of these lines and point of intersection is the solution.

Let us draw graph of $x-y=2$ . As some points on the line are

$(0,2)$ , $(5,7)$ and $(-8,-6)$ , the graph appears as

graph{(x-y+2)(x^2+(y-2)^2-0.04)((x-5)^2+(y-7)^2-0.04)((x+8)^2+(y+6)^2-0.04)=0 [-20, 20, -10, 10]}

Similarly, some points on $2x+y=6$ are $(0,6)$ , $(4,-2)$ and $(-1,8)$ and graph appears as

graph{(2x+y-6)(x^2+(y-6)^2-0.04)((x-4)^2+(y+2)^2-0.04)((x+1)^2+(y-8)^2-0.04)=0 [-20, 20, -10, 10]}

The point of intersection is given by the graph below

graph{(2x+y-6)(x-y+2)=0 [-9.625, 10.375, -2.32, 7.68]}

i.e. Solution is $(4/3,10/3)$

How do you solve x-y=-2x-y=-2, 2x+y=62x+y=6 by graphing?