Question

How do you solve the simultaneous equations `2x+3y=6` and `3x-2y=22`?

Answer 1

`{ (x=6), (y = -2) :}`

Explanation:

Simply multiply the first equation thoroughly by `2` and the second equation by `3` and subtract the results...

After the described multiplication, we get the result as

`4x + 6y = 12`
`9x - 6y = 66`
`stackrel("---------------------------")`

`13x = 78 implies x = 78/13 = 6`

Putting the value of `y` into the first equation, we have

`2 * 6 + 3y = 6`

`3y = 6 - 12`

`3y = -6 implies x = ((-6))/3 = -2`