Question

Solve the system using substitution. Check your solution.
2x - y= 65
5y = x

Answer 1

Answer:

The solutions to the system of equations are:

$x=\frac{325}{9},\:y=\frac{65}{9}$

Step-by-step explanation:

Given the system of the equations

$\begin{bmatrix}2x-y=65\\ 5y=x\end{bmatrix}$

isolate 'x' for 2x-y

$2x-y=65$

Add y to both sides

$2x-y+y=65+y$

$2x=65+y$

Divide both sides by 2

$\frac{2x}{2}=\frac{65}{2}+\frac{y}{2}$

$x=\frac{65+y}{2}$

$\mathrm{Subsititute\:}x=\frac{65+y}{2}$

isolate 'y' for  $5y=\frac{65+y}{2}$

$5y=\frac{65+y}{2}$

$10y=65+y$

subtract y from both sides

$10y-y=65+y-y$

$9y=65$

Divide both sides by 9

$\frac{9y}{9}=\frac{65}{9}$

$y=\frac{65}{9}$

$\mathrm{For\:}x=\frac{65+y}{2}$

$\mathrm{Subsititute\:}y=\frac{65}{9}$

$x=\frac{65+\frac{65}{9}}{2}$

$x=\frac{325}{9}$

The solutions to the system of equations are:

$x=\frac{325}{9},\:y=\frac{65}{9}$