Question

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

Answer 1

Explanation:

The ys have to have the same value. That allows you to equate the right side of each y to each other.

-x^2 + 4 = 2x + 1 Subtract the right side from the left side.

-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1 Combine

-x^2 - 2x + 3 = 0 Multiply both sides by - 1

-1(-x^2 - 2x + 3) = 0*-1 Remove the brackets

x^2 + 2x - 3 Factor

(x - 1)(x + 3 )

x - 1 = 0

x = 1

x + 3 = 0

x = - 3

So the line goes through x = 1 or x = - 3

x = 1

y = 2x + 1

y = 2(1) + 1

y = 3

x = - 3

y = 2(-3) + 1

y = - 6 + 1

y = - 5

Does the graph confirm this? See below.

red: y = -x^2 + 4

green: y = 2x + 1

Yes the graph is in agreement.