WEBVTT

1
00:00:00.000 --> 00:00:08.441
Here is the problem: 9x plus 5y equals 15; negative 5x minus 9y equals 29.

2
00:00:08.890 --> 00:00:11.909
2 linear equations in 2 unknowns (x, y).

3
00:00:12.709 --> 00:00:18.781
Write every equation in standard form. Move all variable terms to the left and constants to the right.

4
00:00:19.231 --> 00:00:23.515
Build the augmented matrix [A | b]. Columns: x, y | constant.

5
00:00:23.965 --> 00:00:30.455
Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column.

6
00:00:30.905 --> 00:00:32.902
Divide R1 by 9.

7
00:00:33.702 --> 00:00:36.454
Clear column 1 using the pivot in R1.

8
00:00:36.904 --> 00:00:40.561
Divide R2 by negative 56 over 9.

9
00:00:41.011 --> 00:00:43.867
Clear column 2 using the pivot in R2.

10
00:00:44.317 --> 00:00:46.163
Reduced row-echelon form.

11
00:00:46.963 --> 00:00:48.681
Read off the unique solution.

12
00:00:49.481 --> 00:00:54.009
So the answer is x equals 5, y equals negative 6.

13
00:00:54.459 --> 00:00:59.881
The system has exactly one solution; substituting it back satisfies every equation.

14
00:01:00.681 --> 00:01:05.813
Equation 1: 9x plus 5y equals 15, which checks out.

15
00:01:06.263 --> 00:01:12.590
Equation 2: negative 5x minus 9y equals 29, which checks out.