Question

Solve the following system of equations using elimination. A. (4, 2)B. (2, 16)C. (-2, 16)D. (16, -2)

Answer 1

A. (4, 2)

Explanation:

Given the system of equations:

`\begin{gathered} x+3y=10\cdots(1) \\ 6x+12y=48\cdots(2) \end{gathered}`

In order to use the elimination method, multiply the first equation by 6 to make the coefficients of x the same.

`\begin{gathered} 6x+18y=60\cdots(3) \\ 6x+12y=48\cdots(2) \end{gathered}`

Subtract equation (2) from equation (3).

`\begin{gathered} 6y=12 \\ \text{Divide both sides by 6} \\ y=(12)/(6) \\ y=2 \end{gathered}`

Next, solve for x using any of the equations:

`\begin{gathered} x+3y=10 \\ x+3(2)=10 \\ x=10-6 \\ x=4 \end{gathered}`

The solution to the system of equations is (x,y)=(4,2).

Option A is correct.