Question

Which point is a solution to the system of linear equations?y = −x + 4x − 3y = 12? (0, 3) (1, 2) (6, −2) (4, −4)

Answer 1

Given: The system of equations below

$\begin{gathered} y=-x+4 \\ x-3y=12 \end{gathered}$

To Determine: The solution of the system of equations

Solution

Let us combine the two equations

$\begin{gathered} equation1:y=-x+4 \\ equation2:x-3y=12 \end{gathered}$

Substituting equation 1 into equation 2

$\begin{gathered} x-3(-x+4)=12 \\ x+3x-12=12 \\ 4x=12+12 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}$

Substitute x = 6 into equation 1

$\begin{gathered} y=-x+4 \\ y=-6+4 \\ y=-2 \end{gathered}$

Hence, the solution is (6, -2)