Question

What is -7x-6y=4 when x=−3y+8? Solve using substitution, and please explain.

Answer 1

I got:
`x=-4`
`y=4`

Explanation:

We substitute `x` in the first equation with the value of `x` given in the second to get:

`-7(color(red)(-3y+8))-6y=4`

rearrange and solve for `y`:

`21y-56-6y=4`

`15y=60`

`y=60/15=4`

use this value of `y` into the second equation:

`x=-3*4+8=-4`

Answer 2

See answer and process to follow below;

Explanation:

First, Write the equation..

`-7x - 6y = 4 - - - - - -eqn1`

`x = -3y + 8 - - - - - - - - - eqn2`

First! thing you must note is the minus`(-)` sign attached to the `x`

In other not to be confused, you have to re-arrange the given equation..

First starting from `eqn1`

`-7x - 6y = 4 - - - - - -eqn1`

Rearrange the equation it would be like;

`7x + 6y = -4` (Carrying it to the other side which will change the sign!)

Therefore we have....

`7x + 6y = -4 - - - - - - - - - - - - eqn1`

`x = -3y + 8 - - - - - - - - - - - - - - eqn2`

Using; Substitution Method!

Substitute the value of `x` in `eqn2` into `eqn1`

`7x + 6y = -4 - - - - - - - - - - - - eqn1`

`x = color(blue)(-3y + 8)`

`7(color(blue)(-3y + 8)) + 6y = -4`

`-21y + 56 + 6y = -4`

Simplifying...

`-21y + 6y + 56 = - 4`

`-15y + 56 = -4`

Collect like terms...

`-15y = - 4 - 56`

`-15y = -60`

Divide both sides by `-15`

`(-15y)/(-15) = (-60)/(-15)`

`(cancel(-15y) )/cancel(-15) = (cancel-60)/(cancel-15)`

`y = 60/15`

`y = 4`

Substitute the value of `y` into `eqn2`

`x = -3y + 8 - - - - - - - - - - - - - - eqn2`

`x = -3(4) + 8`

`x = -12 + 8`

`x = -4`

Hence we have; `x = - 4 and y = 4`