Use the graph to find the solution of the system of equations {y = x^2 + 6x + 8 {y = x + 4

Essentially when people ask you find the solution to system of equation, there asking at what x value do these to graphs intersect. The easiest way to do this is to get a graphing calculator, or desmos and type in the equation and find where they intersect. Heck, even the question says to solve it with a graph, but I'll demonstrate it algebraically.

One way you can do this is set the equation equal to each other. This is because you want to know at what x-value has the same y-value. So we get:

x^2 + 6x + 8 = x + 4

We can then combine like terms, or move everything to one side. So we get:

x^2 + 5x + 4 = 0.

Then we can use the quadratic formula to solve for x.

x = (-5 + / - sqrt (5^2 - 4 (1) (4))) / (2 (1)

This simplifies into:

(-5 + / - 3) / 2

Finally we add and subtract:

(-5 + 3) / 2 = x = - 1

(-5 - 3) / 2 = x = - 4

And our solution is x = - 1, x = - 4