Question

use the elimination method to solve the system of equations write your answer as ordered pair

Answer 1

Solution:

Given the system of equations below;

$\begin{gathered} 4x+6y=24...(1) \\ 4x-y=10...(2) \end{gathered}$

Applying the elimination method

Eliminating the variable x by subtracting equation (2) from (1)

$\begin{gathered} 4x+6y-(4x-y)=24-10 \\ 4x+6y-4x+y=14 \\ Collect\text{ like terms} \\ 4x-4x+6y+y=14 \\ 7y=14 \end{gathered}$

Divide both sides by 7

$\begin{gathered} \frac{7y}{7}=\frac{14}{7} \\ y=2 \end{gathered}$

Substituting 2 for y into equation (2) to find the value of x

$\begin{gathered} 4x-y=10 \\ 4x-2=10 \\ Collect\text{ like terms} \\ 4x=10+2 \\ 4x=12 \\ Divide\text{ both sides by 4} \\ \frac{4x}{4}=\frac{12}{4} \\ x=3 \end{gathered}$

The solution to the system of equations in ordered pair is

$(3,2)$

To check the solution