Question

Find the solutions to the system of equations.
y=x^2+7x+7
y=x+2

Answer 1

Can someone please work it out step by step?

Answer 2

\(\bf \begin{array}{llll}
{\color{red}{ y}}=x^2+7x+7\\
\bf {\color{red}{ y}}=x+2
\end{array}\implies x^2+7x+7=x+2\)

Answer 3

There's your graph.

The formula being graphed is:

x^2 + 7x + 7

and

x + 2

First intersection point is (-5, -3)

Second intersection point is (-1, 1)

It's hard to see on the graph but you can solve for it as well algebraically.

Your 2 equations are:

y = x^2 + 7x + 7

y = x + 2

Since both expressions on the right of the equal sign are equal to y, you can set them equal to each other to get:

x^2 + 7x + 7 = x + 2

Subtract x and subtract 2 from both sides of the equation to get:

x^2 + 7x - x + 7 - 2 = 0

Combine like terms to get:

x^2 + 6x + 5 = 0

Factor this quadratic equation to get:

(x + 5) + (x + 1) = 0

Solve for x to get:

x = -5

x = -1

Substitute in either equation to solve for y.

When x = -5, y = x + 2 becomes y = -3.

When x = -1, y = x + 2 becomes y = 1.

That gets your your intersection points of (-5, -3) and (-1, 1).

You can also substitute in the other equation to get the same answer.

Example:

y = x^2 + 7x + 2 becomes y = (-5)^2 + 7(-5) + 7 which becomes y = 25 - 35 + 7 which becomes y = -10 + 7 which becomes y = -3.

Answer 4

Thank you guys... ♥

Answer 5

You're welcome again!! Xo!