Solve the following system of equations and show all work.
$y = 2 x^{2}$
$y = - 3 x - 1$

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Solution

Solving the given pair of equations:
Given,
$y = 2 x^{2}$
$y = - 3 x - 1$
Equating the above two equations, we get
$2 x^{2} = - 3 x - 1 \Rightarrow 2 x^{2} + 3 x + 1 = 0$
$\Rightarrow 2 x^{2} + 2 x + x + 1 = 0$ [Factoring by splitting the middle term]
$\Rightarrow 2 x (x + 1) + 1 (x + 1) = 0 \Rightarrow (2 x + 1) (x + 1) = 0 ∴ x = \frac{- 1}{2}, - 1$
Hence, the solutions of the given pair of equations are $- \frac{1}{2}, - 1$ .

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