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# x+y=2y-x=2

graph and find the intersection

### 1 Answer by Expert Tutors

John R. | John R: Math, Science, and History TeacherJohn R: Math, Science, and History Teach...
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Since we have two equal signs, we can create two different equations.  Once we find the two equations, we can graph them ans solve for the intersection.

We have three statements that are equal, x + y, 2y - x, and 2, so we can set any pair of them equal to each other:

x + y = 2y - x or x + y = 2 or 2y - x = 2

I am going to use the second and third equations

x + y = 2 and 2y - x = 2

I am going to convert these equations into slope-intercept from by solving them for y

x + y = 2

x + y - x = 2 - x

y = -x + 2

This equation has a slope of -1 and a y-intercept of 2.  To graph this line, place a point at (0,2), which is the y-intercept.  Since the slope is -1, you can count 1 to the right, down 1 to the point (1,1) and draw a line through the points.

For the second equation I am using:

2y - x = 2

2y - x + x = 2 + x

2y = x + 2

2y/2 = (x + 2)/2

y = (1/2)x + 1

The second equation has a a slope of 1/2 and a y-intercept of 1.  This means that you can place a point at (0,1), then count 2 to the right, 1 up to get a second point.  Now that you have two points, you can draw a line through them.

You should see the lines intersect at approximately (2/3,4/3).