Question

What is the solution to y=5x-7 -3x-2y=-12

Answer 1

Since −3x does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3x to both sides.
y=5x−7 
−2y=3x−12

Divide each term in the equation by −2.
y=5x−7 
y=−3x/2+6

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

(2,3)

Answer 2

$y=5x-7 \\ -3x-2y=-12 \\ \\ \hbox{substitute 5x-7 for y in the 2nd equation:} \\ -3x-2(5x-7)=-12 \\ -3x-10x+14=-12 \\ -13x+14=-12 \ \ \ |-14 \\ -13x=-26 \ \ \ |\div (-13) \\ x=2 \\ \\ y=5x-7=5 \times 2-7=10-7=3 \\ \\ \boxed{(x,y)=(2,3)}$