Question

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

Answer 1

Answer:

$x=\frac{70}{11},\:y=\frac{20}{11}$

Step-by-step explanation:

$\begin{bmatrix}4x+2y=16y\\ y=-\frac{1}{2}x+5\end{bmatrix}$

$\mathrm{Substitute\:}y=-\frac{1}{2}x+5$

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

$Simplify$

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

Isolate x for 3x+10=16(-1/2x+5): $x=\frac{70}{11}$

$\mathrm{For\:}y=-\frac{1}{2}x+5$

$\mathrm{Substitute\:}x=\frac{70}{11}$

$y=-\frac{1}{2}\cdot \frac{70}{11}+5$

$-\frac{1}{2}*\frac{70}{11}+5=\frac{20}{11}$

$y=\frac{20}{11}$

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

$x=\frac{70}{11},\:y=\frac{20}{11}$