Question

What is the solution to the system of equations shown below. Show work
X-5y = 11 3x-5y=11

Answer 1

The solution to the system of equations will be:

`x=0,\:y=-(11)/(5)`

Explanation:

Given the expression

`x - 5y = 11`

`3x - 5y = 11`

solving the expression

`\begin{bmatrix}x-5y=11\\ 3x-5y=11\end{bmatrix}`

Multiplying x-5y = 11 by 3: 3x-15y=33

so

`\begin{bmatrix}3x-15y=33\\ 3x-5y=11\end{bmatrix}`

and

`3x-5y=11`

`-`

`\underline{3x-15y=33}`

`10y=-22`

now solving 10y = -22 for y

`10y=-22`

divide both sides by 10

`(10y)/(10)=(-22)/(10)`

simplify

`y=-(11)/(5)`

For 3x-5y=11 plug in y = -11/5

`3x-15\left(-(11)/(5)\right)=33`

`3x+15\cdot (11)/(5)=33`

`3x+33=33`

Subtract 33 from both sides

`3x+33-33=33-33`

Simplify

`3x=0`

Divide both sides by 3

`(3x)/(3)=(0)/(3)`

Simplify

`x=0`

Thus, the solution to the system of equations will be:

`x=0,\:y=-(11)/(5)`