Example 1 - Use Cramer's Rule to express the solution of a system in Determinant Form

Example:
Analysis of a certain DC network results in the system of equations shown below. Use Cramer's Rules to solve for the so-called loop currents I₁ and I₂.

 6 I₁  - 4 I₂ = 10
-4 I₁ + 6 I₂ = -5

Solution:
Solve with Cramer's Rule...
System determinant
∆ =

6	-4
-4	6

= (6) (6) - (-4) (-4) = 20

∆₁ =

10	-4
-5	6

= (10) (6) - (-4) (-5) = 40

∆₂ =

6	10
-4	-5

= (6) (-5) - (10) (-4) = 10

Finally, by Cramer's Rule...
I₁  = ∆₁ / ∆ = 40 / 20 = 2
I₂ = ∆₂ / ∆ = 10 / 20 = 0.5