To solve the system of equations:
- \(3x + 2y = 2\)
- \(-2x + y = 8\)
You can use the method of substitution or elimination, or you can graph the equations to find the intersection.
First, let's solve the second equation for \(y\): \[ y = 2x + 8 \]
Now, substitute \(y\) in the first equation: \[ 3x + 2(2x + 8) = 2 \]
Expanding this: \[ 3x + 4x + 16 = 2 \] \[ 7x + 16 = 2 \] \[ 7x = 2 - 16 \] \[ 7x = -14 \] \[ x = -2 \]
Now, substitute \(x = -2\) back into the equation for \(y\): \[ y = 2(-2) + 8 = -4 + 8 = 4 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-2, 4) \]
So the answer from the options provided is:
(-2, 4)