First, we are going to find the coefficient determinant; we plug our diagonal values into the formula:

D = (2)(2) – (3)(1) = 4 – 4 = 0

Because we have a D of 0 we don't need to go any further; we know we cannot get set values when D is 0 because the values will have 0 in the denominator.

Example 2

Use Cramer's Rule to find:

D_{x}, D_{y}, x, and y

3x – 4y = 8 2x + 2y = 6

We find D, the coefficient determinant:

We multiply down the diagonal from left to right and then subtract the value we get by multiplying up the diagonal from left to right:

D = (3)(2) – (2)(-4) = 6 – (-8) = 14

Next we find our variable-specific determinants.

This is because to find x's determinant we delete the x values from the matrix and substitute in the = values. Then we use Cramer's Rule as usual with the new values:

D_{x} = (8)(2) – (6)(-4) = 16 – (-24) = 40

Now we can find x:

We work out y's determinant the way we did x's; we remove the y values and substitute in the = values.

Now we use Cramer's Rule:

D_{y} = (3)(6) – (2)(8) = 18 – (16) = 2

Now we find y:

So:

Example 3

Use Cramer's Rule to find:

D_{x}, D_{y}, x, and y

-2x + 3y = 7 4x – 3y = 6

We find D, the coefficient determinant:

We multiply down the diagonal from left to right and then subtract the value we get by multiplying up the diagonal from left to right:

D = (-2)(-3) – (4)(3) = 6 – 12 = -6

To find x's determinant we delete the x values from the matrix and substitute in the = values:

Then we use Cramer's Rule as usual with the new values: