Solve the system of equations
3x+2y=2
−2x+y=8
There are different methods to solve systems of equations, but we will use substitution.
From the second equation, we can solve for y in terms of x:
-2x + y = 8
y = 2x + 8
Then we substitute this expression for y into the first equation:
3x + 2y = 2
3x + 2(2x + 8) = 2
Simplifying:
3x + 4x + 16 = 2
7x = -14
x = -2
Now we can use this value of x to find y:
y = 2x + 8 = 2(-2) + 8 = 4
Therefore, the solution to the system of equations is (-2, 4).