Question

Y=−32x+4and y=23x−7

Answer 1

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

`y=-(12)/(5),\:x=(1)/(5)`

Explanation:

Given the equations

`y=-32x+4;\:y=23x-7`

solving the system of the equations

`\begin{bmatrix}y=-32x+4\\ y=23x-7\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y+32x=4\\ y-23x=-7\end{bmatrix}`

`y-23x=-7`

`-`

`\underline{y+32x=4}`

`-55x=-11`

`\begin{bmatrix}y+32x=4\\ -55x=-11\end{bmatrix}`

`-55x=-11`

`(-55x)/(-55)=(-11)/(-55)`

`x=(1)/(5)`

`\mathrm{For\:}y+32x=4\mathrm{\:plug\:in\:}x=(1)/(5)`

`y+32\cdot (1)/(5)=4`

`\mathrm{Subtract\:}32(1)/(5)\mathrm{\:from\:both\:sides}`

`y+32\cdot (1)/(5)-32\cdot (1)/(5)=4-32\cdot (1)/(5)`

`y=-(12)/(5)`

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

`y=-(12)/(5),\:x=(1)/(5)`