Question 490180
This is a "system of equations" or "simultaneous equations (at least, where I went to school)"
y = x-2 and 
y = -2x+7
Now since y = y, you can just set the two equations equal to each other thus:
x-2 = -2x+7 and solve for x. Add 2x to both sides.
3x-2 = 7 Now add 2 to both sides.
3x = 9 Finally, divide both sides by 3.
x = 3 Now you must replace the x in either of the two given equations and solve for y.
y = -2x+7 Substitute x = 3.
y = -2(3)+7 Evaluate.
y = -6+7
y = 1
The solution is (3, 1)
Another way is to graph the two given equations and find the point of intersection (if any) of the two lines.
{{{y = highlight(x-2)}}}
{{{y = highlight_green(-2x+7)}}}
{{{graph(400,400,-5,5,-5,5,x-2,-2x+7)}}}
The lines intersect at (3, 1)