Question

Solve the following system by substitution -3x+y=-5 and 3x+6y=0

Answer 1

Answer:

$x=\frac{10}{7},\:y=-\frac{5}{7}$

Step-by-step explanation:

$\begin{bmatrix}-3x+y=-5\\ 3x+6y=0\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:-3x+y=-5:\quad x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}x=-\frac{-5-y}{3}\\\\\begin{bmatrix}3\left(-\frac{-5-y}{3}\right)+6y=0\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}5+7y=0\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:5+7y=0:\quad y=-\frac{5}{7}\\\\\mathrm{For\:}x=-\frac{-5-y}{3}\\\\\mathrm{Subsititute\:}y=-\frac{5}{7}\\\\x=-\frac{-5-\left(-\frac{5}{7}\right)}{3}$

$-\frac{-5-\left(-\frac{5}{7}\right)}{3}=\frac{10}{7}\\\\x=\frac{10}{7},\:y=-\frac{5}{7}$