Let's take a look at the graph representing the given system of equations.

We can see that the graphs intersect at two points,

(- 2, - 8)

and

(5, 27) .

Therefore, the system has two solutions. Our answer corresponds to option B.

Showing Our Work

Graphing

In case you want to see the steps we took to graph the system, we have included the process. First we graphed the function

y = x^{2} + 2 x - 8 .

We began by determining the values of

a,

b,

and

c .

y = x^{2} + 2 x - 8 \Leftrightarrow y = 1 x^{2} + 2 x + (- 8)

Therefore,

a = 1,

b = 2,

and

c = - 8 .

Then we identified the axis of symmetry.

x = - \frac{b}{2 a}

SubstituteII

$a = 1$ , $b = 2$

x = - \frac{2}{2 ( 1 )}

▼

Simplify

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

x = - \frac{1}{1}

QuotOne

$\frac{a}{a} = 1$

x = - 1

The axis of symmetry for this function is

x = - 1 .

Next we determined the vertex. The axis of symmetry always intersects the parabola at its vertex. Therefore,

x = - 1

is the

x -

coordinate of the vertex. We used this to determine the corresponding

y -

coordinate.

y = x^{2} + 2 x - 8

Substitute

$x = - 1$

y = (- 1)^{2} + 2 (- 1) - 8

▼

Simplify

NegBaseToPosBase

$(- a)^{2} = a^{2}$

y = 1 + 2 (- 1) - 8

MultPosNeg

$a (- b) = - a \cdot b$

y = 1 - 2 - 8

SubTerms

Subtract terms

y = - 9

The vertex of the function is

(- 1, - 9) .

We then found one more point that lies on the parabola. To do so we used

x = 4 .

y = x^{2} + 2 x - 8

Substitute

$x = 4$

y = 4^{2} + 2 (4) - 8

▼

Simplify

CalcPow

Calculate power

y = 16 + 2 (4) - 8

Multiply

y = 16 + 8 - 8

AddSubTerms

Add and subtract terms

y = 16

The point

(4, 16)

lies on the parabola. Finally, we plotted the axis of symmetry

x = - 1,

the vertex

(- 1, - 9),

and the point

(4, 16) .

We also reflected this point across the axis of symmetry.

Finally we connected the three points with a smooth curve.

Next we graphed the linear function

y = 5 x + 2 .

We identified the values of the slope

m

and the

y -

intercept

b .

y = 5 x + 2

We plotted the

y -

intercept and used the slope to plot another point. Then we connected the points with a straight edge.

The last step was connecting the graphs.

Exercise