Question

How do you solve the simultaneous equations `3x + 4y = 7` and `5x - 2y = 16`?

Answer 1

`(x, y) = (3, -1/2)`

Explanation:

[1]`color(white)("XXXX")` `3x+4y = 7`
[2]`color(white)("XXXX")` `5x-2y = 16`

Multiply [2} by 2 giving
[3]`color(white)("XXXX")` `10x-4y = 32`

Add [1] and [3]
[4]`color(white)("XXXX")` `13x = 39`

Divide both sides by 13
[5]`color(white)("XXXX")` `x = 3`

Substitute `3` for `x` in [1]
[6]`color(white)("XXXX")` `3(3) +4y = 7`

Simplify
[7]`color(white)("XXXX")` `4y = -2`

[8]`color(white)("XXXX")` `y = -1/2`