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# How do you solve simultaneous equations where one is quadratic?

3 years ago

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Juana Hahn

1 Answer

Ante R
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A set of two independent **linear** equations with two unknowns has **one** solution pair.

If one of the equations is quadratic, there will be two solution pairs.

A quadratic equation is solved by finding two solutions, for example x² = 9 has solutions 3 and -3. If there is a **y** unknown involved and another equation given, that means that you first need to figure out what the **y** is. Once you figure it out, you substitute the value (or expression) of **y** into your quadratic equation, and solve it as you would any other quadratic equation: by getting two solutions.

[Note that **y** can also have an exponent ², not necessarily **x**. In this case, first solve for **x**, and substitute its value or expression into the quadratic equation.]

**Example:**

x²+2y+1 = 0

y+3 = -2x

y = -2x-3

x²+2(-2x-3)+1 = 0

x²-4x-6+1 = 0

x²-4x-5 = 0

x₁ = -1, x₂ = 5

y₁ = -2(-1)-3 = 2-3 = -1

y₂ = -2*5-3 = -10-3 = -13

Solutions: (-1, -1), (5, -13)

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