To find the final answer use the following:

x=Dx/D y=Dy/D z=Dz/D

These are used to solve systems of equations using matrices and determinants

Where D is the determinant of the coefficient matrix

Solve the system of equations.

1. 5x-4y=1

3x+2y=5

First you find the determinant which you copy the x’s in a column and the y’s in a column. This gives you (5 -4 and the answer is 22.

3 2)

You then replace the x’s with the answers 1 and 5. So Dx= (1 -4 and the answer is 22.

5 2)

Then replace the y’s with the answers 1 and 5. So Dy= (5 1 and the answer is 22.

3 5)

You then use the formulas from above. X=22/22 which is 1, so x equals 1. Y=22/22 which is 1, so y equals 1.

2. 5x-2y=11

x+3y=9

First you find the determinant which you copy the x’s in a column and the y’s in a column. This gives you (5 -2 and the answer is 17.

1 3)

You then replace the x’s with the answers 11 and 9. So Dx= (11 -2 and the answer is 51

9 3)

Then replace the y’s with the answers 11 and 9. So Dy= (5 11 and the answer is 34.

1 9)

You then use the formulas from above. X=51/17 which is 3, so x equals 3. Y=34/17 which is 2, so y equals 2.