what is cramer's rule and how do i apply it?

Question

Answer 1

First set up 3 equations with x, y, and z.

x + 7y + 0z = 16

5x + 0y + 4z = 12

0x -1y - 1z = 5

We make a 3 X 3 matrix from the coefficients of x, y and z.

1 7 0

5 0 4 Now find the determinant of this matrix. Call this value D. I got D = 39

0 -1 -1

Now make a new 3 X 3 matrix by replacing the x column with the constants.

16 7 0

12 0 4 Now find the determinate of this matrix. Call this value D_x. I got D_x = 288

5 -1 -1

Now make a new 3 X 3 matrix by replacing the y column with the constants.

1 16 0

5 12 4 Now find the determinate of this matrix. Call this value D_y. I got D_y = 48

0 5 -1

Now make a new 3 X 3 matrix by replacing the z column with the constants.

1 7 16

5 0 12 Now find the determinate of this matrix. Call this value D_z. I got D_z = -243

0 -1 5

Now we are ready to find the solution because

x = D_x y = D_y z = D_z

D D D

WARNING: These values are not whole numbers. I left them as improper fractions and checked them by substituting into the original equations. They actually worked. You might want to double check to see that you typed the 3 equations correctly.

Answer 2