Question

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

Answer 1

`x=(10)/(7),\:y=-(5)/(7)`

Explanation:

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

`-(-5-\left(-(5)/(7)\right))/(3)=(10)/(7)\\\\x=(10)/(7),\:y=-(5)/(7)\\\\`