WEBVTT

1
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Here is the problem: xy equals 6; x plus y equals 5.

2
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A nonlinear system of 2 equations in x and y.

3
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Read the system.

4
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Solve equation 2 for x. Equation 2 is linear in x, so x can be written in terms of y.

5
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Substitute into equation 1. This leaves one equation in y; its real roots are y equals 2, y equals 3.

6
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Back-substitute to find x. (x, y) equals (3, 2); (x, y) equals (2, 3).

7
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So the answer is (x, y) equals (2, 3) or (x, y) equals (3, 2).

8
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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.

9
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(2, 3) satisfies both equations, which checks out.

10
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(3, 2) satisfies both equations, which checks out.