# Solve Using a Matrix with Cramer’s Rule 4x+5y=2 5x-3y=21

Represent the system of equations in matrix format.
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 .
Subtract from .
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 .
Subtract from .
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 .
Subtract from .
Find the value of by Cramer’s Rule, which states that . In this case, .
Remove parentheses.
Divide by .
Find the value of by Cramer’s Rule, which states that . In this case, .
Remove parentheses.
Divide by .
The solution to the system of equations using Cramer’s Rule.
Solve Using a Matrix with Cramer’s Rule 4x+5y=2 5x-3y=21