Question

What are the solutions to the following system of equations?


y = x2 + 3x − 7


3x − y = −2

Answer 1

       y = x² + 3x - 7
3x - y = -2

  3x - y = -2
- 3x      - 3x
        -y = -3x - 2
         y = 3x + 2

x² + 3x - 7 = 3x + 2
     - 3x       - 3x
        x² - 7 = 2
           + 7 + 7
             x² = 9
              x = ±3

The solutions to the following system of equations is ±3.

Answer 2

Answer:

$(-3,-7)$ and $(3,11)$

Step-by-step explanation:

we have

$y=x^{2} +3x-7$ -----> equation A

$3x-y=-2$ ------> equation B

we know that

The solution of the system of equations is equal to the intersection point both graphs

Using a graphing tool  

see the attached figure

There are two intersection points

Therefore

The system of equations has two solutions

The solutions of the system of equations are the points $(-3,-7)$ and $(3,11)$