Question

Solve the system of equations:

3x+2y=2
−2x+y=8

(-4, 2)
(-2, 4)
(14, -20)
(4, -2)

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Using the method of substitution:

From the second equation, we can isolate y:
-2x + y = 8
y = 2x + 8

Substituting this expression for y into the first equation:
3x + 2(2x + 8) = 2
3x + 4x + 16 = 2
7x + 16 = 2
7x = -14
x = -2

Substituting this value of x back into the second equation:
-2(-2) + y = 8
4 + y = 8
y = 4

Therefore, the solution to the system of equations is (-2, 4).

Checking the solution in both equations:
3(-2) + 2(4) = 6 + 8 = 14 = 2 (True)
-2(-2) + 4 = 4 + 4 = 8 (True)

The correct answer is (-2, 4).