Question

solve the following system of equations.
-6x - 7y = -24
-3x + 8y = -12
x =

y =

Explanation:

Step1: Eliminate x by multiplying the second equation by 2

Multiply the equation \(-3x + 8y = -12\) by 2: \(2\times(-3x + 8y)=2\times(-12)\), which gives \(-6x + 16y = -24\).

Step2: Subtract the first equation from the new equation

Subtract \(-6x - 7y = -24\) from \(-6x + 16y = -24\): \((-6x + 16y)-(-6x - 7y)=-24-(-24)\). Simplify: \(-6x + 16y + 6x + 7y = -24 + 24\), so \(23y = 0\), then \(y = 0\).

Step3: Substitute y = 0 into the first equation to find x

Substitute \(y = 0\) into \(-6x - 7y = -24\): \(-6x - 7\times0 = -24\), which simplifies to \(-6x = -24\), so \(x = 4\).

Answer:

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