Question

linear systems
solving a system of linear equations using elimination with addition
solve the following system of equations.
$5x + 2y = -4$
$3x - 2y = 20$
$x = \boxed{}$
$y = \boxed{}$

Explanation:

Step1: Add the two equations

Add the equations \(5x + 2y = -4\) and \(3x - 2y = 20\) together. The \(y\)-terms will eliminate:
\((5x + 2y) + (3x - 2y) = -4 + 20\)
Simplify: \(8x = 16\).

Step2: Solve for \(x\)

Divide both sides by 8:
\(x = \frac{16}{8} = 2\).

Step3: Substitute \(x = 2\) into one equation

Use the first equation \(5x + 2y = -4\). Substitute \(x = 2\):
\(5(2) + 2y = -4\)
Simplify: \(10 + 2y = -4\).

Step4: Solve for \(y\)

Subtract 10 from both sides:
\(2y = -4 - 10 = -14\)
Divide by 2: \(y = \frac{-14}{2} = -7\).

Answer:

\(x = 2\), \(y = -7\)