WEBVTT

1
00:00:00.000 --> 00:00:08.255
Here is the problem: negative 2x minus 2y equals 8; 9x plus 8y equals negative 31.

2
00:00:08.705 --> 00:00:11.712
2 linear equations in 2 unknowns (x, y).

3
00:00:12.512 --> 00:00:18.723
Write every equation in standard form. Move all variable terms to the left and constants to the right.

4
00:00:19.173 --> 00:00:23.643
Build the augmented matrix [A | b]. Columns: x, y | constant.

5
00:00:24.093 --> 00:00:30.606
Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column.

6
00:00:31.056 --> 00:00:33.413
Divide R1 by negative 2.

7
00:00:34.213 --> 00:00:36.965
Clear column 1 using the pivot in R1.

8
00:00:37.415 --> 00:00:39.969
Divide R2 by negative 1.

9
00:00:40.419 --> 00:00:43.310
Clear column 2 using the pivot in R2.

10
00:00:43.760 --> 00:00:45.583
Reduced row-echelon form.

11
00:00:46.383 --> 00:00:48.159
Read off the unique solution.

12
00:00:48.959 --> 00:00:53.069
So the answer is x equals 1, y equals negative 5.

13
00:00:53.519 --> 00:00:59.103
The system has exactly one solution; substituting it back satisfies every equation.

14
00:00:59.903 --> 00:01:05.429
Equation 1: negative 2x minus 2y equals 8, which checks out.

15
00:01:05.879 --> 00:01:11.893
Equation 2: 9x plus 8y equals negative 31, which checks out.