Question

Please help! .........

Answer 1

1) When x is 1, y is 4, and vice versa

2) When x is -6, y is 42, and when x is 7, y is 114

3) When x is -2, y is 2, and when x is 8, y is 42

Explanation:

1)

`y=x^2-6x+9`

`y+x=5` which can be rearranged as
`y=5-x`.

Substituting this lone y into the first equation, you get:

`5-x=x^2-6x+9`

Move everything to one side:

`x^2-5x+4=0`

Factor:

`(x-4)(x-1)=0`

`x=1, 4`

`y=4, 1`

2)

`y-30=12x` which can be rearranged as
`y=12x+30`.

`y=x^2+11x-12`

Let's use elimination this time and subtract the first equation from the second:

`0=x^2-x-42`

Factor:

`(x-7)(x+6)=0`

`x=-6, 7`

`y= -42, 114`

3)

`y=x^2-2x+6`

`y=4x+10`

Let's set the two equations equal to each other through substitution:

`x^2-2x-6=4x+10`

Move everything to one side:

`x^2-6x-16=0`

Factor:

`(x-8)(x+2)=0`

`x=-2, 8`

`y= 2, 42`

Hope this helps!