Question

find the solution of the system of equations.
$12x + 8y = -12$
$-2x - 2y = -4$

Explanation:

Step1: Simplify the second equation

We can simplify the second equation \(-2x - 2y=-4\) by dividing each term by \(-2\).
\(\frac{-2x}{-2}+\frac{-2y}{-2}=\frac{-4}{-2}\)
Which simplifies to \(x + y = 2\). We can rewrite this as \(x=2 - y\).

Step2: Substitute \(x = 2 - y\) into the first equation

The first equation is \(12x+8y=-12\). Substitute \(x = 2 - y\) into it:
\(12(2 - y)+8y=-12\)
Expand the left - hand side: \(12\times2-12y + 8y=-12\)
\(24-12y + 8y=-12\)

Step3: Combine like terms and solve for \(y\)

Combine the \(y\) terms: \(24-(12y - 8y)=-12\)
\(24 - 4y=-12\)
Subtract 24 from both sides: \(-4y=-12 - 24\)
\(-4y=-36\)
Divide both sides by \(-4\): \(y=\frac{-36}{-4}=9\)

Step4: Solve for \(x\)

We know that \(x = 2 - y\), and \(y = 9\). So substitute \(y = 9\) into \(x=2 - y\):
\(x=2-9=-7\)

Answer:

The solution of the system of equations is \(x=-7\) and \(y = 9\), or the ordered pair \((-7,9)\)