Question

How do you solve the system of equations `3x - 4y = - 6` and `x - 5y = 9`?

Answer 1

We have,

`3x - 4y = -6`
`x - 5y = 9`

Multiplying the second equation with 3 and subtracting from the first,

`-4y + 15y = -33`
`implies 11y = -33`
`implies y = -3`

Substituting this value in the second equation,

`x = 9 + 5(-3)`
`implies x = 9 - 15`
`implies x = -6`

Thus, the solution is `(-6,-3)`.

Answer 2

`color(red)((x,y)=(-6,-3))`

Explanation:

Given
[1]`color(white)("XXX")3x-4y=-6`
[2]`color(white)("XXX")x-5y=9`

Multiplying [2] by `3` (to make the coefficient of `x` the same as in [1]
[3]`color(white)("XXX")3x-15y=27`

Subtracting [3] from [1]
[4]`color(white)("XXX")11y=-33`

Dividing both sides of [4] by `11`
[5]`color(white)("XXX")y=-`

Substituting `3` for `y` in [1]
[6]`color(white)("XXX")3x-4xx(-3)=-6`

Simplifying
[7]`color(white)("XXX")3x=-6-12`

[8]`color(white)("XXX")3x=-18`

[9]`color(white)("XXX")x=-6`

Therefore `(x,y)=(-6,-3)`