Question

How do you solve the system `-4x+ y =6` and `-5x - y =21` by substitution?

Answer 1

Answer 2

`-4x+ y =6` ----------(1)
`-5x - y =21`----------(2)

We can transpose `-4x` in the first equation to the right hand side:

`y = 4x + 6` ------(3)

Substituting `y` from the third equation into the second one gives us:

`- 5x - (4x+6) = 21`

`-5x - 4x - 6 = 21`

`-9x - 6 = 21`

`-9x = 21+6`

`-9x = 27`

Dividing both sides by `-9` will give us:

`(cancel(-9)x)/cancel(-9) = 27/-9`

`color(green)(x = -3`

Substituting `x = -3` in the third equation will give us :

`y = 4(-3) + 6`

`y = -12 + 6`

`color(green)( y = -6`

The solution to both these equations :`x = -3; y = -6`

Verify :

Substitute the values of `x and y` in both the equations to see if they are satisfied