Question

What is the solution to the linear system 4x + 2y = 8 and 2x + 2y = 2?

Answer 1

• x=3

,

• y=-2

Explanation:

Given the linear system of the equations:

`\begin{gathered} 4x+2y=8\cdots\cdots\cdots(1) \\ 2x+2y=2\cdots\cdots\cdots(2) \end{gathered}`

First, subtract equation(2) from equation(1).

`\begin{gathered} (4x-2x)+(2y-2y)=8-2 \\ 2x=6 \\ \text{Divide both sides by 2} \\ (2x)/(2)=(6)/(2) \\ x=3 \end{gathered}`

Next, substitute x=3 into equation (1) to solve for y.

`\begin{gathered} 4x+2y=8\cdots\cdots\cdots(1) \\ 4(3)+2y=8 \\ 12+2y=8 \\ \text{Subtract 12 from both sides.} \\ 12-12+2y=8-12 \\ 2y=-4 \\ \text{Divide both sides by 2} \\ (2y)/(2)=(-4)/(2) \\ y=-2 \end{gathered}`

The solution to the linear system is x=3 and y=-2.