Question

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

Answer 1

Answer:

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

Step-by-step 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!