Answer :
Answer:
There are two pairs of solutions: (-1,4) and (2,7)
Step-by-step explanation:
We are given the following system of equations:
y = x² + 3
y = x + 5
Equaling both equations:
x² + 3 = x + 5
x² - x + 3 - 5 = 0
x² - x - 2 = 0
Solving the second order equation:
[tex]x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(-2)}}{2}=\frac{1\pm\sqrt[]{9}}{2}=\frac{1\pm3}{2}[/tex]So, the possible values for x are -1 and 2.
When x = -1: y = x + 5 = -1 + 5 = 4
When x = 2: y = x + 5 = 2 + 5 = 7
There are two pairs of solutions: (-1,4) and (2,7)