Question

How do you solve the following system: `3x+2y =0, 7y − 6x − 5 = 0`?

Answer 1

`y = 5/11, x = -10/33`

Explanation:

Rearrange the first equation to give a value of `y` with respect to `x`.

`3x + 2y = 0`
`3x = -2y`
`-3/2x = y`

Now substitute your new value of `y` into the second equation

`7(-3/2x) - 6x - 5 = 0`
`-21/2x - 6x - 5 = 0`
#-33x - 5 = 0

Rearrange and solve for `x`

`-33/2x = 5`
`x = -10/33`

And because we know `y` with respect to `x`, we can solve

`y = -3/2x`
`y = -3/2 * -10/33 = 30/66 = 5/11`

Substitute both values into either original equation and check if it's right.

`3x + 2y = 0`
`-30/33 + 10/11 = 0`

It checks out mathematically, so it must be correct.