WEBVTT

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Here is the problem: x squared plus y squared equals 25; x minus y equals 1.

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A nonlinear system of 2 equations in x and y.

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Read the system.

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Solve equation 2 for x. Equation 2 is linear in x, so x can be written in terms of y.

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Substitute into equation 1. This leaves one equation in y; its real roots are y equals negative 4, y equals 3.

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Back-substitute to find x. (x, y) equals (negative 3, negative 4); (x, y) equals (4, 3).

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So the answer is (x, y) equals (negative 3, negative 4) or (x, y) equals (4, 3).

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Solving one equation for a variable and substituting turns the system into a single equation in one unknown; each root gives one solution pair.

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(negative 3, negative 4) satisfies both equations, which checks out.

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(4, 3) satisfies both equations, which checks out.