Question

x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)

Answer 1

I would solve the first equation for x and then sub that value into x in the second equation.  That's the easiest way.  x - 2y = 3 solved for x is x = 2y+3.  Now sub that in for x in the second equation: 5(2y+3)+3y=2 and 10y + 15 + 3y = 2.  13y = -13, and y = -1.  Now sub that y value into either equation to solve for x: x = 2(-1) + 3 gives us an x value of x = 1.  Therefore, your solution to this system is (1, -1), first choice above.