Question

What is `y` and `x` when `y= 2x-11` and `y= x- 8` ?

Answer 1

x = + 3 y = -5

Explanation:

One way to solve the problem is to subtract the two equations from each other.

# y = 2x - 11 - (y = x - 8 )#

`y-y = 0`
`2x - x = x`
`- 11 -( -8) = -3`

so `y = 2x - 11 - ( y = x -8) = { 0 = x - 3}`

Solving for `0 = x -3` add 3 to both sides giving

`0 + 3 = x -3 + 3` so

`+3 = x`

now put the value of +3 into either equation and solve for y

`y = +3 -8`

`y = -5`

To check put these values into the second equation

`-5 = 2(+3) - 11`

`-5 = +6 -11`

# -5 = -5 check

x = +3 y = -5

Answer 2

`color(red)(y=-5,x=3`

Explanation:

`y=2x-11` ------(1)

`y=x-8` ---------(2)

`(2) xx 2`

`2y=2x-16` ------(3)

`(1)-(3)`

`-y=5`

`color(red)(y=-5`

substitute `color(red)(y=-5` in (2)

`color(red)(-5)=x-8`

`x-8=-5`

`x=-5+8`

`color(red)(x=3`

substitute`color(red)(y=-5,x=3` in (1)

`color(red)(-5)=2(color(red)3)-11`

`-5=6-11`

`-5=-5`