Q8. - Algebra 1

Question

Use elimination to solve the system.

$\begin{array}{c}\mathbf{6}\mathbf{x}\mathbf{-}\mathbf{4}\mathbf{y}\mathbf{=}\mathbf{6}\\ \mathbf{-}\mathbf{6}\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{y}\mathbf{=}\mathbf{0}\end{array}$

A  $\mathbf{(}\mathbf{5}\mathbf{,}\mathbf{6}\mathbf{)}$

B  $\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{6}\mathbf{)}$

C $\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{0}\mathbf{)}$ 

D $\mathbf{(}\mathbf{4}\mathbf{,}\mathbf{-}\mathbf{8}\mathbf{)}$

Step-by-Step Solution

Answer

The solution of the given system of equations is $\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{6}\mathbf{)}$. Therefore, the option B is correct.

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{c}6x-4y=6...\left(1\right)\\ -6x+3y=0....\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Add the equations (1) and (2) to eliminate the variable $x$.

$\begin{array}{l}6x-4y=6\\ -6x+3y=0\\ \overline{-y=6}\\ y=-6\end{array}$

The value $y$ of is $-6$.

Substitute $-6$ for $y$ in the equation (1) to find the value of $x$.

$\begin{array}{c}6x-4y=6\\ 6x-4(-6)=6\\ 6x+24=6\\ 6x=6-24\\ 6x=-18\\ x=\frac{-18}{6}\\ x=-3\end{array}$

The value of $x$ is $-3$.

Therefore, the solution of the given system of equations is  $(-3,-6)$.

Therefore, the option $B$ is correct.