WEBVTT

1
00:00:00.000 --> 00:00:08.208
Here is the problem: 2x minus 3y equals 4; negative 3x plus 8y equals negative 6.

2
00:00:08.658 --> 00:00:11.700
2 linear equations in 2 unknowns (x, y).

3
00:00:12.500 --> 00:00:18.595
Write every equation in standard form. Move all variable terms to the left and constants to the right.

4
00:00:19.045 --> 00:00:23.236
Build the augmented matrix [A | b]. Columns: x, y | constant.

5
00:00:23.686 --> 00:00:30.211
Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column.

6
00:00:30.661 --> 00:00:32.403
Divide R1 by 2.

7
00:00:33.203 --> 00:00:35.920
Clear column 1 using the pivot in R1.

8
00:00:36.370 --> 00:00:38.855
Divide R2 by 7 over 2.

9
00:00:39.305 --> 00:00:42.208
Clear column 2 using the pivot in R2.

10
00:00:42.658 --> 00:00:44.597
Reduced row-echelon form.

11
00:00:45.397 --> 00:00:47.104
Read off the unique solution.

12
00:00:47.904 --> 00:00:51.793
So the answer is x equals 2, y equals 0.

13
00:00:52.243 --> 00:00:57.955
The system has exactly one solution; substituting it back satisfies every equation.

14
00:00:58.755 --> 00:01:03.887
Equation 1: 2x minus 3y equals 4, which checks out.

15
00:01:04.337 --> 00:01:10.212
Equation 2: negative 3x plus 8y equals negative 6, which checks out.