Question

How do you solve the following system?: `y = 3/4x + 5 , x + 2y = 3`

Answer 1

`x=-14/5` and `y=29/10`

Explanation:

From the given equations
`y=(3x)/4+5` and `x+2y=3`

Using the second equation `x+2y=3`
Let `x=3-2y` then substitute in the first equation

first equation becomes

`y=(3(3-2y))/4+5`

multiply both sides by of the equation by 4 now to get rid of any fraction

`4y=4*(3(3-2y))/4+4*5`

`4y=cancel4*(3(3-2y))/cancel4+4*5`

`4y=9-6y+20`

`4y+6y=9+20`

`10y=29`
divide both sides by 10

`(10y)/10=29/10`

`(cancel10y)/cancel10=29/10`

`y=29/10`

Solve now for the value of x using the second equation

`x=3-2y` and `y=29/10`

`x=3-2*(29/10)`
`x=3-29/5`
`x=(15-29)/5`

`x=-14/5`

God bless...I hope the explanation is useful..