Question

Algebra Il v14 (GS) / Module 06: Systems of Equations and Inequalities1.(06.01)Solve the following system of equations and show all work.y = x2 + 3y = x + 5 (10 points)

Answer 1

There are two pairs of solutions: (-1,4) and (2,7)

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:

`x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(-2)}}{2}=\frac{1\pm\sqrt[]{9}}{2}=(1\pm3)/(2)`

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)