Question

Solve the following system of equations and show all work. y = 2x2 y = –3x −1

Answer 1

Answer:

(- 1, 2) and (- $\frac{1}{2}$, $\frac{1}{2}$)

Step-by-step explanation:

Given the 2 equations

y = 2x² → (1)

y = - 3x - 1 → (2)

Substitute y = 2x² into (2)

2x² = - 3x - 1 ( add 3x and 1 to both sides )

2x² + 3x + 1 = 0 ← in standard form

(2x + 1)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - $\frac{1}{2}$

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = - 1 → y = - 3(- 1) - 1 = 3 - 1 = 2 ⇒ (- 1, 2 )

x = - $\frac{1}{2}$ → y = $\frac{3}{2}$ - 1 = $\frac{1}{2}$ ⇒ (- $\frac{1}{2}$, $\frac{1}{2}$ )