WEBVTT

1
00:00:00.000 --> 00:00:08.638
Here is the problem: 7x plus 4y equals 32 over 3; 6x minus 4y equals 24.

2
00:00:09.088 --> 00:00:12.118
2 linear equations in 2 unknowns (x, y).

3
00:00:12.918 --> 00:00:19.083
Write every equation in standard form. Move all variable terms to the left and constants to the right.

4
00:00:19.533 --> 00:00:23.817
Build the augmented matrix [A | b]. Columns: x, y | constant.

5
00:00:24.267 --> 00:00:30.966
Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column.

6
00:00:31.416 --> 00:00:33.378
Divide R1 by 7.

7
00:00:34.178 --> 00:00:36.953
Clear column 1 using the pivot in R1.

8
00:00:37.403 --> 00:00:40.921
Divide R2 by negative 52 over 7.

9
00:00:41.371 --> 00:00:44.169
Clear column 2 using the pivot in R2.

10
00:00:44.619 --> 00:00:46.419
Reduced row-echelon form.

11
00:00:47.219 --> 00:00:48.879
Read off the unique solution.

12
00:00:49.679 --> 00:00:54.927
So the answer is x equals 8 over 3, y equals negative 2.

13
00:00:55.377 --> 00:01:00.938
The system has exactly one solution; substituting it back satisfies every equation.

14
00:01:01.738 --> 00:01:07.636
Equation 1: 7x plus 4y equals 32 over 3, which checks out.

15
00:01:08.086 --> 00:01:13.763
Equation 2: 6x minus 4y equals 24, which checks out.