Question

Solve the system of equations using substitution
4x + 2y = 16
=−12+5

Answer 1

`x=(70)/(11),\:y=(20)/(11)`

Explanation:

`\begin{bmatrix}4x+2y=16y\\ y=-(1)/(2)x+5\end{bmatrix}`

`\mathrm{Substitute\:}y=-(1)/(2)x+5`

`\begin{bmatrix}4x+2\left(-(1)/(2)x+5\right)=16\left(-(1)/(2)x+5\right)\end{bmatrix}`

`Simplify`

`\begin{bmatrix}3x+10=16\left(-(1)/(2)x+5\right)\end{bmatrix}`

Isolate x for 3x+10=16(-1/2x+5):
`x=(70)/(11)`

`\mathrm{For\:}y=-(1)/(2)x+5`

`\mathrm{Substitute\:}x=(70)/(11)`

`y=-(1)/(2)\cdot (70)/(11)+5`

`-(1)/(2)*(70)/(11)+5=(20)/(11)`

`y=(20)/(11)`

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

`x=(70)/(11),\:y=(20)/(11)`