WEBVTT

1
00:00:00.000 --> 00:00:07.071
Here is the problem: x squared plus y squared equals 25; x plus y equals 7.

2
00:00:07.521 --> 00:00:10.760
A nonlinear system of 2 equations in x and y.

3
00:00:11.560 --> 00:00:12.512
Read the system.

4
00:00:12.962 --> 00:00:19.382
Solve equation 2 for x. Equation 2 is linear in x, so x can be written in terms of y.

5
00:00:19.832 --> 00:00:28.284
Substitute into equation 1. This leaves one equation in y; its real roots are y equals 3, y equals 4.

6
00:00:28.734 --> 00:00:35.607
Back-substitute to find x. (x, y) equals (4, 3); (x, y) equals (3, 4).

7
00:00:36.407 --> 00:00:42.374
So the answer is (x, y) equals (3, 4) or (x, y) equals (4, 3).

8
00:00:42.825 --> 00:00:52.206
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
00:00:53.006 --> 00:00:56.582
(3, 4) satisfies both equations, which checks out.

10
00:00:57.032 --> 00:01:00.689
(4, 3) satisfies both equations, which checks out.