Solve the system of equations.
y = 2x² - 3, y = -3x - 1

Solution:

Given:

Equations are y = 2x² - 3 --- (1)

y = -3x - 1 --- (2)

Substitute equation (2) in (1)

⇒ -3x - 1 = 2x² - 3

⇒ 2x² + 3x - 2 = 0

⇒ 2x² + 4x - x - 2 = 0

⇒ 2x(x + 2) - 1(x + 2) = 0

⇒ (2x - 1)(x + 2) = 0

⇒ 2x -1 = 0

⇒ x = 1/2 and x = -2

Substitute x = 1/2 in equation (1)

y = 2(1/2)² - 3

y = 1/2 - 3 = -5/2

⇒ x + 2 = 0 ⇒ x = -2

Substitute x = -2 in equation (1)

y = 2(2)² - 3

y = 8 - 3 = 5

Solutions are (1/2, -5/2) and (-2, 5).

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Solve the system of equations.
y = 2x² - 3, y = -3x - 1

Summary:

The solutions for the system of equations y = 2x² - 3, y = -3x - 1 are (1/2, -5/2) and (-2, 5).