Question

I don’t understand this

Answer 1

The solution to the system of linear equations

`y=4,\:x=2`

i.e. (x, y) = (2, 4)

The graph is also attached.

Explanation:

Given the system of linear equations

`y=3x-2`

`y-2=x`

solving the system

`\begin{bmatrix}y=3x-2\\ y-2=x\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y-3x=-2\\ y-x=2\end{bmatrix}`

`y-x=2`

`-`

`\underline{y-3x=-2}`

`2x=4`

solve for x

`2x=4`

Divide both sides by 2

`(2x)/(2)=(4)/(2)`

`x=2`

`\mathrm{For\:}y-3x=-2\mathrm{\:plug\:in\:}x=2`

`y-3\cdot \:2=-2`

`y-6=-2`

`y=4`

Thus, the solution to the system of linear equations

`y=4,\:x=2`

i.e. (x, y) = (2, 4)

The graph is also attached.