Question

Solve the linear system given explicitly or by its augmented matrix. Show details.

4x-6y=-11

-3y+8z=10

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	b
1	4	-6	-11
2	-3	8	10

Make the pivot in the 1st column by dividing the 1st row by 4

	X1	X2	b
1	1	-3/2	-11/4
2	-3	8	10

Eliminate the 1st column

	X1	X2	b
1	1	-3/2	-11/4
2	0	7/2	7/4

Make the pivot in the 2nd column by dividing the 2nd row by 7/2

	X1	X2	b
1	1	-3/2	-11/4
2	0	1	1/2

Eliminate the 2nd column

	X1	X2	b
1	1	0	-2
2	0	1	1/2

Solution set:

x = -2

y = 1/2