Question

If four times a first number is decreased by three times the second number, the result is zero. The sum of the numbers is -7. Find the numbers?

Answer 1

`-3, and, -4.`

Explanation:

By what is given,

`4N_1-3N_2=0...(1), and, N_1+N_2=-7...(2).`

`(2) rArr 3(N_1+N_2)=-21, i.e., 3N_1+3N_2=-21...(2').`

`(1)+(2') rArr 4N_1+3N_1=0+(-21),`

`rArr 7N_1=-21 rArr N_1=-21/7=-3," &, by (2), then, "N_2=-4.`

Answer 2

`-3` and `-4`

Explanation:

Let's say the first number is `x` and the second number is `y`

So, first we're told that `4*x-3*y=0` and then, that `x+y=-7`

Let's use substitiution!

Our first job is to set `x+y=-7` to `x`:
`x+y=-7`
subtract `y` on both sides
`x=-7-y`

Now, substitute `x` for `(-7-y)` in the firstequation:
`4x-3y=0`
`4(-7-y)-3y=0`
distribute the `4`
`-28-4y-3y=0`
add `28` on both sides
`-4y-3y=28`
combine like-terms
`-7y=28`.
divide by `-7` on both sides
`y=-4`

Now that we know `y=-4`, we can solve for `x`:
`x+y=-7`
`x+(-4)=-7`
add `4` on both sides
`x=-3`

Just to double-check our work, let's solve the first equation using `-3` and `-4` as `x`and `y`
`4x-3y=0`

If our answers are correct, we should find our solution to be `0`!
`4(-3)-3(-4)`
`-7--7`
`-7+7`
`0=0`
We were right!