We are given a system of two linear equations with two variables, $x$ and $y$: $-5x + y = -7$ $-3x - 2y = -12$ The goal is to solve for $x$ and $y$.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$-5x + y = -7$

$-3x - 2y = -12$

The goal is to solve for $x$ and $y$.

2. Solution Steps

We can use the substitution or elimination method. Let's use the elimination method.

Multiply the first equation by 2:

$2(-5x + y) = 2(-7)$

$-10x + 2y = -14$

Now we have:

$-10x + 2y = -14$

$-3x - 2y = -12$

Add the two equations to eliminate $y$:

$(-10x + 2y) + (-3x - 2y) = -14 + (-12)$

$-13x = -26$

Divide by -13:

$x = \frac{-26}{-13}$

$x = 2$

Now substitute $x = 2$ into the first equation $-5x + y = -7$:

$-5(2) + y = -7$

$-10 + y = -7$

$y = -7 + 10$

$y = 3$

So the solution is $x = 2$ and $y = 3$.

We can verify the solution by plugging $x=2$ and $y=3$ into the second equation:

$-3x - 2y = -12$

$-3(2) - 2(3) = -6 - 6 = -12$

The equation holds true.

3. Final Answer

$x = 2, y = 3$