Question

solve the following system of equations.
$5x - 3y = -12$
$2x - 5y = -20$
$x = \square$
$y = \square$

Explanation:

Step1: Eliminate one variable (e.g., x)

Multiply the first equation by 2: \(2(5x - 3y)=2(-12)\) gives \(10x - 6y=-24\).
Multiply the second equation by 5: \(5(2x - 5y)=5(-20)\) gives \(10x - 25y=-100\).

Step2: Subtract the two new equations

\((10x - 6y)-(10x - 25y)=-24-(-100)\)
Simplify: \(10x - 6y - 10x + 25y=-24 + 100\)
\(19y = 76\)

Step3: Solve for y

Divide both sides by 19: \(y=\frac{76}{19}=4\)

Step4: Substitute y=4 into first equation

\(5x - 3(4)=-12\)
\(5x - 12=-12\)

Step5: Solve for x

Add 12 to both sides: \(5x=0\)
Divide by 5: \(x = 0\)

Answer:

\(x = 0\)
\(y = 4\)