Question

Look at the system of equations below.

{y = − 2 x + 3
4 x − 3y = 11
What is the solution to the system? Show your work.

Answer 1

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=2,\:y=-1`

Explanation:

Considering the system of the equation

`\begin{bmatrix}y=-2x+3\\ 4x-3y=11\end{bmatrix}`

`\mathrm{Subsititute\:}y=-2x+3`

`\begin{bmatrix}4x-3\left(-2x+3\right)=11\end{bmatrix}`

`\mathrm{Isolate}\:x\:\mathrm{for}\:4x-3\left(-2x+3\right)=11`

`4x-3\left(-2x+3\right)=11`

`4x+6x-9=11`

`10x-9=11`

`10x-9+9=11+9`

`10x=20`

`x=2`

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

`\mathrm{Subsititute\:}x=2`

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

`y=-1`

`\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}`

`x=2,\:y=-1`