Question

What are the solutions to the system of equations?

y=x^2+5x+6,
y=3x+6

A. (0, 6) and (−2, 0)
B. (−3, 0) and (0, 6)
C. (−3, 0) and (−2, 0)
D. (0, −3) and (6, 0)

Answer 1

you can just plug in the x’s to find the y’s.

for example, you can plug in (0,6) into y=x^2+5x+6 by placing the 0 from the point where the x’s are to see if it gives you 6 (the ‘y’ term in the point)

this would look like y=(0)^2+5(0)+6

when you type this in, if it gives you 6 as the answer, then (0,6) is a solution

Answer 2

A. (0, 6) and (−2, 0)

Explanation:

The given equations are:

`y=x^2+5x+6`

and

`y=3x+6`

We equate the two equations to find their point of intersection;

`x^2+5x+6=3x+6`

We equate everything to zero to get;

`x^2+2x=0`

`x(x+2)=0`

`x=0,x=-2`

When x=0, y=3(0)+6=6

One solution is;

(0,6)

When x=-2,

y=3(-2)+6=0

Another solution is;

(-2,0)