Question

2x - 3y = 9
-5x – 3y = 30
Elimination method

Answer 1

The solution to the system of the equations be:

• (x, y) = (-3, -5)

Explanation:

Given the system of equations

`2x - 3y = 9`

`-5x - 3y = 30`

Solving the system of equations using the elimination method

Multiply
`2x-3y=9` by 5:
`10x-15y=45`

Multiply
`-5x-3y=30` by 2:
`-10x-6y=60`

`\begin{bmatrix}10x-15y=45\\ -10x-6y=60\end{bmatrix}`

adding the equations

`-10x-6y=60`

`+`

`\underline{10x-15y=45}`

`-21y=105`

now solving -21y = 105 for y

`-21y=105`

Divide both sides by -21

`(-21y)/(-21)=(105)/(-21)`

Simplify

`y=-5`

For 10x - 15y = 45 plug in y = -5

`10x-15\left(-5\right)=45`

Apply the rule -a(-a) = a

`10x+15\cdot \:5=45`

`10x+75=45`

Subtract 75 from both sides

`10x+75-75=45-75`

Simplify

`10x=-30`

Divide both sides by 10

`(10x)/(10)=(-30)/(10)`

Simplify

`x=-3`

Therefore, the solution to the system of the equations be:

• (x, y) = (-3, -5)

The graph of the solution to the system of equations is also attached below.