Answer:
x = 2, y = -5
Step-by-step explanation:
There are many ways to solve a system of equations. In this case, I chose the substitution method.
1) First, isolate a variable in either one of the equations. I chose to isolate y in the equation -7x + y = -19.
[tex]-7x +y = -19\\y = 7x -19[/tex]
2) Since we know that y = 7x - 19 from that equation, we can substitute for y in the other equation. Substitute the y in -2x + 3y = -19 for 7x - 19 and solve for x:
[tex]-2x + 3(7x-19) = -19\\-2x + 21x - 57=-19\\19x - 57 = -19\\19x = 38\\x = 2[/tex]
Thus, x = 2.
3) Then, in order to find y, take that answer and substitute for x in any one of the equations. I chose -7x + y = -19 in this case, substituting 2 for x and solving for y:
[tex]-7(2) + y = -19\\-14 + y = -19\\y = -5[/tex]
Thus, y = -5. Therefore, the answer is x = 2 and y = -5.
