Question

use elimination to solve the system of equations.
$3x + 2y = -19$
$-3x - 5y = 25$
(\boxed{\quad}, \boxed{\quad})

Explanation:

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

We have the system:
\[

$$\begin{cases} 3x + 2y = -19 \\ -3x - 5y = 25 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((3x + 2y)+(-3x - 5y)=-19 + 25\)
Simplify the left - hand side: \(3x-3x+2y - 5y=-3y\)
Simplify the right - hand side: \(6\)
So we get the equation \(-3y=6\)

Step2: Solve for \(y\)

From \(-3y = 6\), divide both sides by \(-3\):
\(y=\frac{6}{-3}=-2\)

Step3: Substitute \(y = - 2\) into one of the original equations to solve for \(x\)

Substitute \(y=-2\) into the first equation \(3x + 2y=-19\):
\(3x+2\times(-2)=-19\)
Simplify: \(3x-4=-19\)
Add \(4\) to both sides: \(3x=-19 + 4=-15\)
Divide both sides by \(3\): \(x=\frac{-15}{3}=-5\)

Answer:

\((-5,-2)\)