Question

How do you solve the system of equations `8x + 4y = 84` and `9x - 9y = 54`?

Answer 1

`x=9, \ \ y=3`

Explanation:

Given equations

`8x+4y=84`

`2x+y=21\ ..........(1)` &

`9x-9y=54`

`x-y=6\ ..........(2)`

Adding (1) & (2), we get

`2x+y+x-y=21+6`

`3x=27`

`x=27/3`

`x=9`

setting `x=9` in (1), we get

`2(9)+y=21`

`y=21-18`

`y=3`

hence the solution of given equations is

`x=9, \ \ y=3`

Answer 2

Let's solve the first equation first

`8x+4y=84`

All you have to do is take out the value of a variable

Let's take out the value of `y` both `x` and `y` will be irritating in the next equation but `y` will be less irritating (maybe)

Factorize out 4 and divide

`4(2x+y)=84`

`2x+y=21`

`color(red)(y=21-2x`

Now to the second equation

`9x-9y=54`

Factorize out `9`

`9(x-y)=54`

`x-y=6`

Put value of `y`

`x-(21-2x)=6`

Notice that after opening the brackets the values will go from plus to minus and from minus to plus

`x-21+2x=6`

`3x-21=6`

`3x=6+21`

`3x= 27`

`x=27/3`

`color(darkorange)(x=9`

`y=21-2x`

`y=21-2xx9`

`y=21-18`

`color(darkorange)(y=3`

Answer 3

`x=9` and `y=3`

Explanation:

`9*(8x+4y)+4*(9x-9y)=9*84+4*54`

`72x+36y+36x-36y=756+216`

`108x=972`, so `x=972/108=9`

Thus,

`9*9-9y=54`

`81-9y=54`

`-9y=-27`

`y=(-27)/(-9)=3`