Question

(8x- y=3
(4x+ 5y = 15​

Answer 1

`x=(15)/(22)`

`y=(27)/(11)`

Explanation:

Given system of equations:

A)
`8x-y=3`

B)
`4x+5y=15`

To solve for
`x` and
`y`

Using substitution method to solve the system.

Rearranging equation A, to solve for
`y` in terms of
`x`

Subtracting both sides by
`3`

`8x-y-3=3-3`

`8x-y-3=0`

Adding
`y` both sides.

`8x-y+y-3=0+y`

`8x-3=y`

So, we have
`y=8x-3`

Substituting value of
`y` we got from A into equation B.

`4x+5(8x-3)=15`

Using distribution.

`4x+40x-15=15`

Simplifying.

`44x-15=15`

Adding 15 both sides.

`44x-15+15=15+15`

`44x=30`

Dividing both sides by 44.

`(44x)/(44)=(30)/(44)`

Simplifying fractions.

∴
`x=(15)/(22)` (Answer)

We can plugin
`x=(15)/(22)` in the rearranged equation A to get value of
`y`

`y=8((15)/(22))-3`

`y=(120)/(22)-3`

Simplifying fractions.

`y=(60)/(11)-3`

Making whole numbers to fractions.

`y=(60)/(11)-(3)/(1)`

Taking LCD = 11 to subtract fractions

`y=(60)/(11)-(33)/(11)`

`y=(60-33)/(11)`

∴
`y=(27)/(11)` (Answer)