Question

solve the system of linear equations by elimination.
$3x - 2y = 4$
$6x - 2y = -2$
solution: (\square, \square)

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 3x - 2y = 4 \\ 6x - 2y = -2 \end{cases}$$

Subtract the first equation from the second equation to eliminate \(y\):
\((6x - 2y)-(3x - 2y)=-2 - 4\)
Simplify the left - hand side: \(6x-2y - 3x + 2y=3x\)
Simplify the right - hand side: \(-6\)
So we get \(3x=-6\)

Step2: Solve for x

Divide both sides of the equation \(3x = - 6\) by 3:
\(x=\frac{-6}{3}=-2\)

Step3: Substitute x into one of the original equations

Substitute \(x = - 2\) into the first equation \(3x-2y = 4\):
\(3\times(-2)-2y = 4\)
Simplify the left - hand side: \(-6-2y = 4\)
Add 6 to both sides: \(-2y=4 + 6=10\)
Divide both sides by - 2: \(y=\frac{10}{-2}=-5\)

Answer:

\((-2,-5)\)