Question

How do you solve the following system?: `2x - 4y = 5 , x-4y=3`

Answer 1

I found:
`x=2`
`y=-1/4`

Explanation:

I would isolate `x` from the second equation and substitute it into the first:
`x=3+4y`
and so:
`2(color(red)(3+4y))-4y=5` solve for `y`:
`6+8y-4y=5`
`4y=-1`
`y=-1/4`
Substitute this back into: `x=3+4y`
`x=3+4(color(red)(-1/4))=3-1=2`

Answer 2

Use substitution for `x` then plug back in with `y`.

Explanation:

If `x - 4y = 3`, then add `4y` to both sides to get `x = 4y + 3`.

Knowing this, you can plug in `4y + 3` in the other equation in place of `x` since they are equivalent.

This results in: `2(4y + 3) - 4y = 5`
Distribute the 2 to get: `8y + 6 - 4y = 5`
Combine like terms on the left: `4y + 6 = 5`
Subtract 6 from both sides: `4y = -1`
Divide both sides by 4: `color(red)(y = -1/4)`

With this knowledge, plug `y` into either equation to determine the value of `x`, as such: `x - 4(-1/4) = 3`
Multiply (remember that a negative time a negative is positive): `x + 1 = 3`
Add 1 to both sides: `color(red)(x = 2)`

Thus, our ordered pair is `(2, -1/4)`.