Question

find the solution of the system of equations.

$-2x - 3y = -28$
$-2x + 2y = 22$

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system:

$$
LATEXBLOCK0
$$

Subtract equation \((2)\) from equation \((1)\):

$$
LATEXBLOCK1
$$

Step2: Solve for \(y\)

Divide both sides of \(-5y = -50\) by \(-5\):

$$ y = \frac{-50}{-5} = 10 $$

Step3: Substitute \(y = 10\) into one of the original equations to solve for \(x\)

Let's use equation \((2)\): \(-2x + 2y = 22\)
Substitute \(y = 10\):

$$
LATEXBLOCK2
$$

Answer:

The solution of the system is \(x = -1\) and \(y = 10\), or in ordered pair form \((-1, 10)\)