Question

How do you solve the following system?: `16x +13y =7, -19x +15y = -2`

Answer 1

`x = 131/7`

`y = -(2047)/91`

Explanation:

1. `16x+13y = 7`
2. `15y - 19x =-2`

In equation 1, make `y` the subject.

`13y = 7-16x -> y = (7-16x)/13`

Inject that into equation 2.

`15((7-16x)/13) - 19x = -2`

Solve for `x`.

`(105-240x)/13 -19x = -2`

`(105-240x)/13 = 19x - 2`

`105 -240x = 247x - 26`

`247x-240x = 105+26`

`7x = 131`

`x = 131/7`

Inject the value `x` into the rearranged equation 1 to calculate the value of `y`.

`y = (7-16(131/7))/13`

`y = -(2047)/91`

Answer 2

`x=131/487`
`y=101/487`

Explanation:

`16x+13y=7`
`-19x+15y=-2`

Multiply top equation by `15` and second linear equation by `13` to make the values of `y` the same so they cancel out when subtracted from each other:

`240x+195y=105`
`-247x+195y=-26`
which gives:
`487x=131` when subtracted from each other.
`x=131/487`

Substitute `x` into first original equation:

`16(131/487)+13y=7`
`(2096/487)+13y=7`
`13y=7-(2096/487)`
`13y=(1313/487)`
`y=((1313/487))/13`
`y=101/487`