Question

1. -6x - y = 8\\12x + 4y = -8

Explanation:

Step1: Solve the first equation for y

From \(-6x - y = 8\), we can rewrite it as \(y=-6x - 8\).

Step2: Substitute y into the second equation

Substitute \(y = -6x - 8\) into \(12x + 4y=-8\). So we have \(12x+4(-6x - 8)=-8\).

Step3: Simplify the equation

First, expand the left - hand side: \(12x-24x - 32=-8\).
Then, combine like terms: \(-12x-32 = - 8\).
Add 32 to both sides: \(-12x=-8 + 32\), which simplifies to \(-12x = 24\).
Divide both sides by - 12: \(x=\frac{24}{-12}=-2\).

Step4: Find the value of y

Substitute \(x = - 2\) into \(y=-6x - 8\). Then \(y=-6\times(-2)-8\).
Calculate: \(y = 12-8 = 4\).

Answer:

The solution of the system of equations is \(x=-2\) and \(y = 4\).