Question

Need to find X and Y
x=3y+7
x=2y-1

please explain how you came up with your answer

Answer 1

You make the assumption that the x from equation 1 is the same as the x from equation 2 somewhere in the plane, and so you set them equal to each other but write each x in terms of y:

3y+7=2y-1
3y-2y=-1-7
y=-8

after solving for y, you find x by substituting -8 for y in either of the two original equations (I choose the second equation):

x=2(-8)-1=-16-1=-17

the geometric interpretation of a unique solution of a system of equations is the point of intersection between the two lines, so the solution set can be written as

{(-17,-8)}