Question

Solve the system of equations 4x+6y=−84x+6y=−8 and 2x+y=122x+y=12 by combining the equations.

Answer 1

Given the system of equations:

`\begin{gathered} 4x+6y=-8\ldots(1) \\ 2x+y=12\ldots(2) \end{gathered}`

Multiply equation (2) with 2.

`4x+2y=24\ldots(3)`

Subtract (3) from (1) and solve for y.

`\begin{gathered} 4y=-32 \\ y=-(32)/(4)=-8 \end{gathered}`

Substitute the obtained value of y into (2) to find x.

`\begin{gathered} 2x-8=12 \\ 2x=20 \\ x=(20)/(2)=10 \end{gathered}`

The solution of the system of equations is

x = 10, y = -8