# Finite Math Examples

Solve Using a Matrix with Cramer's Rule
,
Step 1
Represent the system of equations in matrix format.
Step 2
Find the determinant of .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Step 3
Find the determinant of .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Step 4
Find the determinant of .
These are both valid notations for the determinant of a matrix.
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Step 5
Find the value of by Cramer's Rule, which states that . In this case, .
Remove parentheses.
Move the negative in front of the fraction.
Step 6
Find the value of by Cramer's Rule, which states that . In this case, .
Remove parentheses.
Move the negative in front of the fraction.
Step 7
The solution to the system of equations using Cramer's Rule.
Step 8