WEBVTT

1
00:00:00.000 --> 00:00:09.195
Here is the problem: 9x plus 4y equals negative 55; negative 8x plus 8y equals negative 32.

2
00:00:09.645 --> 00:00:12.919
2 linear equations in 2 unknowns (x, y).

3
00:00:13.719 --> 00:00:19.942
Write every equation in standard form. Move all variable terms to the left and constants to the right.

4
00:00:20.392 --> 00:00:24.665
Build the augmented matrix [A | b]. Columns: x, y | constant.

5
00:00:25.115 --> 00:00:31.767
Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column.

6
00:00:32.218 --> 00:00:34.296
Divide R1 by 9.

7
00:00:35.096 --> 00:00:37.801
Clear column 1 using the pivot in R1.

8
00:00:38.251 --> 00:00:41.734
Divide R2 by 104 over 9.

9
00:00:42.184 --> 00:00:45.028
Clear column 2 using the pivot in R2.

10
00:00:45.478 --> 00:00:47.336
Reduced row-echelon form.

11
00:00:48.136 --> 00:00:49.785
Read off the unique solution.

12
00:00:50.585 --> 00:00:55.252
So the answer is x equals negative 3, y equals negative 7.

13
00:00:55.702 --> 00:01:01.240
The system has exactly one solution; substituting it back satisfies every equation.

14
00:01:02.040 --> 00:01:07.764
Equation 1: 9x plus 4y equals negative 55, which checks out.

15
00:01:08.214 --> 00:01:14.414
Equation 2: negative 8x plus 8y equals negative 32, which checks out.