Solve 2x-3y4 and x 4y 3 by matrix method?

2x - 3y = 4

x + 4y = 3

Write the augmented matrix:

2 -3 4

1 4 3

Multiply the first row by 1/2:

1 -3/2 2

1 4 3

Subtract the second row from the first row:

1 - 3/2 2

0 -11/2 -1

Multiply the second row by -2/11:

1 -3/2 2

0 1 2/11

Multiply the second row by 3/2 and add it to the first row:

1 0 25/11

0 1 2/11

Thus x = 25/11 and y = 2/11

Check: