Question

How do you solve the system of equations `8x - 2y = 48` and `3x - 4y = 1`?

Answer 1

`7 4/13 and y = 5 3/13`

Explanation:

One method of solving a system of equations is by eliminating one of the variables.

The best scenario is to have additive inverses.
The sum of additive inverses is 0. `-3x + 3x = 0`

`color(white)(xxxxxxxxx)8x -2y = 48` .....................A
`color(white)(xxxxxxxxx)3x -4y = 1` ........................B

Let's create additive inverses with the `y-`terms

`A xxcolor(red)(-2): -16xcolor(red)(+4y)=-96` ...............C
`color(white)(xxxxxx.x.x)3xcolor(red)( -4y) = 1` ........................B

Adding the equations will eliminate the y terms.

`C+B: color(white)(xxxx)-13x = -95`

`color(white)(xxxxxxxxxxxxx) x = 7 4/13`

Now find y,
Substitute `7 4/13` for `x` in B

`3 (95/13) -4y = 1`

`285/13 -1 = 4y`

`(285 -13)/(13 xx 4) = y`

`272/52 = y`

`5 3/13 = y`