Question

find the solution of the system of equations.\

$$\begin{cases}2x - 5y = -12\\\\-3x + 5y = 13\\end{cases}$$

\
show your work here\
x = \
y = \
check

Explanation:

Step1: Add the two equations

Add the equations \(2x - 5y = -12\) and \(-3x + 5y = 13\) together. The \(-5y\) and \(+5y\) will cancel out.

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Step2: Solve for x

Multiply both sides of \(-x = 1\) by \(-1\) to solve for \(x\).

$$ x = -1 $$

Step3: Substitute x into one equation

Substitute \(x = -1\) into the first equation \(2x - 5y = -12\).

$$ 2(-1) - 5y = -12 $$

Step4: Solve for y

Simplify the left side: \(-2 - 5y = -12\). Add 2 to both sides:

$$ -5y = -12 + 2\\ -5y = -10 $$

Divide both sides by \(-5\):

$$ y = \frac{-10}{-5} = 2 $$

Answer:

\(x = -1\), \(y = 2\)