Question

How do you solve `3x + 5y = 2` and `9x + 11y = 14`?

Answer 1

There are several ways to do this. First you have to get rid of one of the letters:

Explanation:

Multiply everything in the first equation by `3` and then subtract the second equation:

`9x+15y=6` minus
`9x+11y=14`
`0x+4y=-8->4y=-8->y=-2`

Subsitute the `y`-value in one of the original equations:
`3x+5(-2)=2->3x-10=2->3x=12->x=4`

To check your answer, you may substitute both values in the other equation:
`9*4+11*(-2)=36-22=14` Check!

Answer 2

`(x,y)=(4-2)`

Explanation:

Given
[1]`color(white)("XXX")3x+5y=2`
[2]`color(white)("XXX")9x+11y=14`

Notice that multiplying [1] by `3` will produce a coefficient for `x` equal to that of equation [2].
We could then subtract equation [2] to get an equation in only `y`
`{:([1]xx3,rarr,9x+15y=6),([2],"-",9x+11y=14),([3],"=",bar(color(white)("XXX")4y=-8)) :}`

Dividing both sides by `4` gives
[5]`color(white)("XXX")y=-2`

Substituting `(-2)` for `y` back into equation [1]:
[6]`color(white)("XXX")3x+5xx(-2)=2`

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

[8]`color(white)("XXX")x=4`