Question

How do you solve the system `4x + y = 6` and `6x + 3y = 6`?

Answer 1

Try to eliminate `y` by expressing it in terms of `x` in two ways from the two original equations.

With the first equation, subtract `4x` from both sides to get:

`y = 6 - 4x`

With the second equation, first divide through by 3 to get

`2x+y = 2`

Then subtract `2x` from both sides to get

`y = 2 - 2x`

Now we have two expressions both equal to `y`, so we can put them together:

`6 - 4x = y = 2 - 2x`

So `6 - 4x = 2 - 2x`

Add `4x` to both sides to get

`6 = 2 + 2x`

Subtract 2 from both sides to get

`4 = 2x`

Then divide both sides by 2 to get

`2 = x`, that is `x = 2`.

Then looking back at one of our previous equations:

`y = 2 - 2x = 2 - 2*2 = 2-4 = -2`

Answer 2

You first express `y` as function of `x`, then solve for `x`

`4x+y=6->y=6-4x`

Substitute this in the other equation:
`6x+3y=6->6x+3*(6-4x)=6->`
`6x+18-12x=6->-6x=-12->x=2`

Now put this `x` into the first equation:
`y=6-4x=6-4*2=-2`

Answer:
`x=2`
`y=-2`