Question

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

Answer 1

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} (7y)/(7)=(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} \\ (4x)/(4)=(12)/(4) \\ x=3 \end{gathered}`

The solution to the system of equations in ordered pair is

`(3,2)`

To check the solution