Question

Question #bbb03

Answer 1

You solve this as a systems of equations.

Explanation:

Start by multiplying the entire equation of `y=4x-7` by `7` and the entire equation of `y=-7x+15` by `4`. Now you have:

`7y=28x-49" "` and `" "4y=-28x+60`

Line them up vertically:

`7y=28x-49`
`4y=-28x+60`

and subtract them, so the `x`'s cancel out. You now should have

`3y=11`

Divide both sides by `3` to get `y` by itself, and you get

`y = 11/3.`

Now, plug in `11/3` for `y` into the original equation and solve for `x`:

`11/3=4x-7" "` (add `7` to both sides to cancel it)

`32/3=4x " "` (divide both sides by `4` to cancel it)

`8/3 = x`

BAM! You're done!

Answer 2

`x=2 and y=1`

Explanation:

This is the best form to have when solving a system of equations,!

They both show `y` in terms of `x`.

We know that `color(red)(y = y)`

So, the expressions that are both equal to `y` must be equal!

`color(white)(xxxx)color(red)(y = y)`

`color(red)(4x-7 = -7x+15)" "larr` solve for `x`

`4x +7x = 15+7`

`11x = 22`

`x = 2`

Substitute `2` for `x` in both equations to check that you get the same answer.

`y = 4x -7" "and" "y = -7x+15`

`y = 4(2) -7" "and" "y = -7(2)+15`

`y = 8-7" "and " "y = -14+15`

In both cases `y=1`