Question

Solve the following system of equations using matrices.

4x - 2y = 1

5x + y = 10

Answer 1

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

	X1	X2	b
1	4	-2	1
2	5	1	10

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

	X1	X2	b
1	1	-1/2	1/4
2	5	1	10

Eliminate the 1st column

	X1	X2	b
1	1	-1/2	1/4
2	0	7/2	35/4

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

	X1	X2	b
1	1	-1/2	1/4
2	0	1	5/2

Eliminate the 2nd column

	X1	X2	b
1	1	0	3/2
2	0	1	5/2

Solution set:

x = 3/2

y = 5/2