Question

How do you solve this system of equations using the substitution method `x- y = 1 and 4x + 9y = - 87`?

Answer 1

`y=-7`
`x=-6`

Explanation:

Given -

`x-y=1` ----------------(1)
`4x+9y=-87` ----------(2)
Solve equation (1) for `x`
`x=1+y`
Substitute `x=1+y` in equation (2)
`4(1+y)+9y=-87`
`4+4y+9y=-87`
`13y=-87-4=-91`
`y=(-91)/13=-7`

`y=-7`

Substitute `y=-7` in equation (1)

`x-(-7)=1`
`x+7=1`
`x=1-7=-6`

`x=-6`

Answer 2

`x=-6 and y=-7`

Explanation:

Here ,

`x-y=1 =>x=y+1.....to(1)`

`4x+9y=-87.................to(2)`

Substitute value of `x` from`(1)` into `(2)`

`4(y+1)+9y=-87`

`4y+4+9y=-87`

`13y=-91`

`:.color(red)(y=-7`

Subst. `color(red)(y=-7` into (1)

`x=color(red)(-7)+1=>color(blue)(x=-6`

Hence , `x=-6 and y=-7`