Question

How do you solve the simultaneous equations `2x + 3y = 9` and `3x + 2y = 1`?

Answer 1

Multiply each equation by a (different) constant so the coefficients of `x` (or `y`) are identical then subtract one equation from the other to isolate a single variable.
`(x, y) = (-3, 5)`

Explanation:

[1]`color(white)("XXXX")` `2x+3y = 9`
[2]`color(white)("XXXX")` `3x+2y=1`

Multiply [1] by 2 and [2] by 3 to get
[3]`color(white)("XXXX")` `4x+6y =18`
[4]`color(white)("XXXX")` `9x+6y = 3`

Subtract [4] from [3]
[5]`color(white)("XXXX")` `-5x = 15`

Solve for `x` by dividing [5] by `(-5)`
[6]`color(white)("XXXX")` `x = -3`

Substitute `(-3)` for `x` in [1] to solve for `y`
[7]`color(white)("XXXX")` `2(-3) + 3y = 9`

[8]`color(white)("XXXX")` `3y = 15`

[9]`color(white)("XXXX")` `y = 5`