# Finite Math Examples

Solve Using a Matrix with Cramer's Rule
, ,
Move all terms containing variables to the left side of the equation.
Move to the left side of the equation because it contains a variable.
Move to the left side of the equation because it contains a variable.
Move to the left side of the equation because it contains a variable.
Move to the left side of the equation because it contains a variable.
Represent the system of equations in matrix format.
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Multiply by .
Since the matrix is multiplied by , the determinant is .
Subtract from .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Multiply by .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Multiply by .
Since the matrix is multiplied by , the determinant is .
The determinant of is .
Set up the determinant by breaking it into smaller components.
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Subtract from .
Multiply by .
The determinant of is .
The determinant of a matrix can be found using the formula .
Simplify the determinant.
Simplify each term.
Multiply by .
Multiply by .
Simplify the expression.
Multiply by .
Since the matrix is multiplied by , the determinant is .
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the parentheses from the numerator.
Divide by .
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the parentheses from the numerator.
Divide by .
Find the value of by Cramer's Rule, which states that . In this case, .
Remove the parentheses from the numerator.
Divide by .
The solution to the system of equations using Cramer's Rule.