Question

solve the following system of equations.
$2x + 5y = -4$
$-2x + 3y = 20$

Explanation:

Step1: Eliminate x by adding equations

Add the two equations: \((2x + 5y) + (-2x + 3y) = -4 + 20\)
Simplify: \(8y = 16\)

Step2: Solve for y

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

Step3: Substitute y into first equation

Substitute \(y = 2\) into \(2x + 5y = -4\): \(2x + 5(2) = -4\)
Simplify: \(2x + 10 = -4\)

Step4: Solve for x

Subtract 10: \(2x = -14\)
Divide by 2: \(x = -7\)

Answer:

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