WEBVTT

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Here is the problem: y equals x squared; y equals x plus 2.

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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 1 for y. Equation 1 is linear in y, so y can be written in terms of x.

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Substitute into equation 2. This leaves one equation in x; its real roots are x equals negative 1, x equals 2.

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Back-substitute to find y. (x, y) equals (negative 1, 1); (x, y) equals (2, 4).

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So the answer is (x, y) equals (negative 1, 1) or (x, y) equals (2, 4).

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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 1, 1) satisfies both equations, which checks out.

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