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 variablespecific 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:
