Question

6x - 3y = 12\
y = -6x - 12

Explanation:

Step1: Substitute \( y = -6x - 12 \) into \( 6x - 3y = 12 \)

Substitute the expression for \( y \) from the second equation into the first equation. So we get \( 6x - 3(-6x - 12) = 12 \).

Step2: Simplify the left - hand side

First, distribute the - 3 in \( -3(-6x - 12) \): \( -3\times(-6x)=18x \) and \( -3\times(-12) = 36 \). So the equation becomes \( 6x+18x + 36=12 \).
Then combine like terms: \( 6x+18x=24x \), so \( 24x+36 = 12 \).

Step3: Solve for \( x \)

Subtract 36 from both sides of the equation: \( 24x=12 - 36=-24 \).
Then divide both sides by 24: \( x=\frac{-24}{24}=-1 \).

Step4: Solve for \( y \)

Substitute \( x = - 1 \) into \( y=-6x - 12 \). Then \( y=-6\times(-1)-12=6 - 12=-6 \).

Answer:

The solution of the system of equations is \( x=-1,y = - 6 \)