# Finite Math Examples

Solve Using a Matrix with Cramer's Rule
,
Step 1
Move all of the variables to the left side of each equation.
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Subtract from both sides of the equation.
Step 1.4
Reorder and .
Step 2
Represent the system of equations in matrix format.
Step 3
Find the determinant of the coefficient matrix .
Step 3.1
Write in determinant notation.
Step 3.2
The determinant of a matrix can be found using the formula .
Step 3.3
Simplify the determinant.
Step 3.3.1
Simplify each term.
Step 3.3.1.1
Multiply by .
Step 3.3.1.2
Multiply .
Step 3.3.1.2.1
Multiply by .
Step 3.3.1.2.2
Multiply by .
Step 3.3.2
Subtract from .
Step 4
Since the determinant is not , the system can be solved using Cramer's Rule.
Step 5
Find the value of by Cramer's Rule, which states that .
Step 5.1
Replace column of the coefficient matrix that corresponds to the -coefficients of the system with .
Step 5.2
Find the determinant.
Step 5.2.1
The determinant of a matrix can be found using the formula .
Step 5.2.2
Simplify the determinant.
Step 5.2.2.1
Simplify each term.
Step 5.2.2.1.1
Multiply by .
Step 5.2.2.1.2
Multiply .
Step 5.2.2.1.2.1
Multiply by .
Step 5.2.2.1.2.2
Multiply by .
Step 5.2.2.2
Subtract from .
Step 5.3
Use the formula to solve for .
Step 5.4
Substitute for and for in the formula.
Step 5.5
Dividing two negative values results in a positive value.
Step 6
Find the value of by Cramer's Rule, which states that .
Step 6.1
Replace column of the coefficient matrix that corresponds to the -coefficients of the system with .
Step 6.2
Find the determinant.
Step 6.2.1
The determinant of a matrix can be found using the formula .
Step 6.2.2
Simplify the determinant.
Step 6.2.2.1
Simplify each term.
Step 6.2.2.1.1
Multiply by .
Step 6.2.2.1.2
Multiply .
Step 6.2.2.1.2.1
Multiply by .
Step 6.2.2.1.2.2
Multiply by .
Step 6.2.2.2
Subtract from .
Step 6.3
Use the formula to solve for .
Step 6.4
Substitute for and for in the formula.
Step 6.5
Dividing two negative values results in a positive value.
Step 7
List the solution to the system of equations.