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

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

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 $(-2,0)$

Answer 2

Answer:

(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