Question

What are the solutions (coordinate points) to the system of equations?

y = x^2 + 5x + 6 and y = 3x + 6
Show work please :) ​

Answer 1

(0,6) & (-2,0)

Step-by-step explanation:

y = x² + 5x + 6

y = 3x + 6

x² + 5x + 6 = 3x + 6

x² + 2x = 0

x(x + 2) = 0

x = 0, -2

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

x = -2, y = 3(-2)+6 = 0

Answer 2

The solutions of the system of equations are
`(0,6)` and
`(-2,0)`

Step-by-step explanation:

Given that the system of equations are
`y = x^2 + 5x + 6` and
`y = 3x + 6`

We need to determine the solution to the system of equations.

Let us determine the solution to the system of equations using substitution method.

Thus, we have,

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

Subtracting both sides of the equation by 6, we get,

`x^(2) +5x=3x`

Subtracting both sides of the equation by 3x, we have,

`x^(2) +2x=0`

Simplifying, we get,

`x(x+2)=0`

Thus, the values of x are
`x=0` and
`x=-2`

Now, we shall determine the corresponding y - values.

Substituting
`x=0` in the equation
`y = 3x + 6`, we get,
`y=6`

Similarly, substituting
`x=-2` in the equation
`y = 3x + 6`, we get,
`y=0`

Therefore, the solution to the system of equations are
`(0,6)` and
`(-2,0)`