Solve the following system of equations and show all work.
y=-x² + 4, y=2x+1

Solution:

y = -x² + 4

y = 2x + 1

These linear equations can be solved by using elimination or substitution method

As both the equations are equal to y, the two equations are equal to one another.

-x² + 4 = 2x + 1

By further calculation

4 - 1 = 2x + x²

It can be written as

x² + 2x = 3

x² + 2x - 3 = 0

(x + 3) (x - 1) = 0

So we get

x = -3 or 1

Substituting the value of x in either of the equations

y = 2x + 1 or y = 2x + 1

y = 2 (-3) + 1 or y = 2 (1) + 1

y = - 6 + 1 or y = 2 + 1

y = -5 or y = 3

Therefore, the ordered pairs are (-3, -5) and (1, 3).

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Solve the following system of equations and show all work.

Summary:

Solving the following system of equations, the ordered pairs are (-3, -5) and (1, 3).