We are given a system of two linear equations: $y = -3x + 2$ $y = x - 2$ We need to find the solution to this system, which is the point $(x, y)$ that satisfies both equations.

1. Problem Description

We are given a system of two linear equations:

$y = -3x + 2$

$y = x - 2$

We need to find the solution to this system, which is the point $(x, y)$ that satisfies both equations.

2. Solution Steps

We can use the substitution method to solve this system of equations. Since both equations are already solved for $y$, we can set them equal to each other:

$-3x + 2 = x - 2$

Now, we solve for $x$:

$-3x - x = -2 - 2$

$-4x = -4$

$x = \frac{-4}{-4}$

$x = 1$

Now that we have found the value of $x$, we can substitute it into either of the original equations to find the value of $y$. Let's use the second equation:

$y = x - 2$

$y = 1 - 2$

$y = -1$

Therefore, the solution to the system of equations is $(1, -1)$.

3. Final Answer

The solution to the system of equations is $(1, -1)$.