SOLUTION: Solve this system of equations by graphing: x – 2y = -2 x + 2y = 6

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Question 127480: Solve this system of equations by graphing:
x – 2y = -2
x + 2y = 6

Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
x-2y=-2 or -2y=-x-2 or y=-x/-2-2/-2 or y=x/2+1 (red line)
x+2y=6 or 2y=-x+6 or y=-x/2+6/2 or y=-x/2+3 (green line)
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%2F2+%2B1%2C+-x%2F2+%2B3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions x/2 +1 and -x/2 +3).
THE ANSWER IS(2,2)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

1x-2y=-2
1x%2B2y=6




In order to graph these equations, we need to solve for y for each equation.



So let's solve for y on the first equation

1x-2y=-2 Start with the given equation


-2y=-2-x Subtract +x from both sides


-2y=-x-2 Rearrange the equation


y=%28-x-2%29%2F%28-2%29 Divide both sides by -2


y=%28-1%2F-2%29x%2B%28-2%29%2F%28-2%29 Break up the fraction


y=%281%2F2%29x%2B1 Reduce


Now lets graph y=%281%2F2%29x%2B1 (note: if you need help with graphing, check out this solver)


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x%2B1%29+ Graph of y=%281%2F2%29x%2B1



So let's solve for y on the second equation

1x%2B2y=6 Start with the given equation


2y=6-x Subtract +x from both sides


2y=-x%2B6 Rearrange the equation


y=%28-x%2B6%29%2F%282%29 Divide both sides by 2


y=%28-1%2F2%29x%2B%286%29%2F%282%29 Break up the fraction


y=%28-1%2F2%29x%2B3 Reduce



Now lets add the graph of y=%28-1%2F2%29x%2B3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x%2B1%2C%28-1%2F2%29x%2B3%29+ Graph of y=%281%2F2%29x%2B1(red) and y=%28-1%2F2%29x%2B3(green)

From the graph, we can see that the two lines intersect at the point (2,2)