Question

how can i get an elimination out of this equation

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given system of equations

$\begin{gathered} 8x-y=24 \\ -2x+y=0 \end{gathered}$

STEP 2: Solve the equations to get x

$\begin{gathered} 8x-y=24---\text{equation 1} \\ -2x+y=0----\text{equation 2} \\ \text{Add equation 1 to equation 2} \\ 8x+(-2x)-y+(+y)=24+0 \\ 8x-2x-y+y=24 \\ 6x=24 \\ \text{Divide both sides by 6} \\ \frac{6x}{6}=\frac{24}{6} \\ x=4 \end{gathered}$

STEP 3: Substitute for x in equation 1 to get y

$\begin{gathered} 8x-y=24 \\ x=4 \\ By\text{ substitution,} \\ 8(4)-y=24 \\ 32-y=24 \\ -y=24-32 \\ -y=-8 \\ \text{Divide both sides by -1} \\ -\frac{y}{-1}=-\frac{8}{-1} \\ y=8 \\ \\ \text{Therefore, we have:} \\ (4,8) \end{gathered}$

Hence, the solution to the equation is

$(4,8)$

OPTION A