Using a graphing utility, find the exact solutions of the system. round to the nearest hundredth and choose a solution to the system from the choices below.
y = x² + 3x
y = 2x + 5

(0,4)
(2.79, 0.58)
(1.79, 8.58)
(-0.58, -2.79)

Part 1) The exact solutions are

  and  

Part 2) (1.79, 8.58)

Step-by-step explanation:

we have

----> equation A

----> equation B

we know that

When solving the system of equations by graphing, the solution of the system is the intersection points both graphs

Find the exact solutions of the system

equate equation A and equation B

The formula to solve a quadratic equation of the form

is equal to

in this problem we have

so

substitute in the formula

so

The solutions are

Find the values of y

First solution

For

The first solution is the point

Second solution

For

The second solution is the point

Round to the nearest hundredth

First solution

----->

----->

see the attached figure to better understand the problem

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.