Question

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

Answer 1

`x = 3`
`y = 1/2`

Explanation:

`x + 2y = 4`
`3x - 4y = 7`

Solve the first equation for `x`
`x = 4 - 2y`

Substitute the value of `x` into the second equation.
`3(4 - 2y) - 4y = 7`

Now there is only one variable present, so we can solve for `y`.
`12 - 6y - 4y = 7`
`- 10y = 7 - 12`
`y = (-5/-10)`
`y = 1/2`

Finally, substitute the value of `y` into the first equation again
`x + 2 * 1/2 = 4`
`x + 1 = 4`
`x = 4 - 1 = 3`#