Question

How do you solve the simultaneous equations `4x + y = 9` and `2x - y = 3`?

Answer 1

Since both given equations contain similar coefficients for `y`, the simplest method is to add the two equations and solving single variable equations to get
`(x,y) =(2,1)`

Explanation:

[1]`color(white)("XXXX")` `4x+y = 9`
[2]`color(white)("XXXX")` `2x-y = 3`

Add [1] to [2] giving
[3]`color(white)("XXXX")` `6x = 12`
Divide both sides by `6`
[4]`color(white)("XXXX")` `x = 2`
Using information from [4], replace `x` with `2` in [1]
[5]`color(white)("XXXX")` `4(2)+y = 9`
Simplify
[6]`color(white)("XXXX")` `y=1`