To solve this system of equations, we can use substitution or elimination method. Here's the solution using the substitution method:
y + 2 = 3(x - 1) (1)
y = -2x + 10 (2)
We can substitute equation (2) into equation (1) for y:
(-2x + 10) + 2 = 3(x - 1)
Simplifying this equation, we get:
-2x + 12 = 3x - 3
Adding 2x to both sides, we get:
12 = 5x - 3
Adding 3 to both sides, we get:
15 = 5x
Dividing both sides by 5, we get:
x = 3
Now, we can substitute x = 3 into equation (2) to find the value of y:
y = -2(3) + 10
y = 4
Therefore, the solution to the system of equations is (x, y) = (3, 4).