Question

4x-3y=1
5x+4y=9
What are the resulting equations?

Answer 1

x = 1; y = 1

Explanation:

First thing we will do is work with the first equation:

`4x - 3y = 1`

`4x = 1+3y`

`x = (3)/(4) y~+~(1)/(4)`

Now that we have a value for x, we insert that into the second equation, like so:

`5((3)/(4)y~+~(1)/(4)) + 4y = 9`

`(15)/(4)y~+~(5)/(4) + 4y = 9`

`(15)/(4)y~+~4y~+~(5)/(4) = 9`

`(15)/(4)y~+~(16)/(4) y~+~(5)/(4)`

`(31)/(4)y~+~(5)/(4) =9`

`31y + 5 = 9 * 4`

`31y + 5 = 36`

`31y = 36-5`

`31y = 31`

`y = (31)/(31)`

`y = 1`

Now, we solve for x:

`4x - 3(1) = 1`

`4x - 3 = 1`

`4x = 1 + 3`

`4x = 4`

`x = (4)/(4)`

`x=1`

Hope it helped,

BiologiaMagister