Question

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

Answer 1

The solutions to the system of equations are:

`x=(325)/(9),\:y=(65)/(9)`

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

`(2x)/(2)=(65)/(2)+(y)/(2)`

`x=(65+y)/(2)`

`\mathrm{Subsititute\:}x=(65+y)/(2)`

isolate 'y' for
`5y=(65+y)/(2)`

`5y=(65+y)/(2)`

`10y=65+y`

subtract y from both sides

`10y-y=65+y-y`

`9y=65`

Divide both sides by 9

`(9y)/(9)=(65)/(9)`

`y=(65)/(9)`

`\mathrm{For\:}x=(65+y)/(2)`

`\mathrm{Subsititute\:}y=(65)/(9)`

`x=(65+(65)/(9))/(2)`

`x=(325)/(9)`

The solutions to the system of equations are:

`x=(325)/(9),\:y=(65)/(9)`