Use Cramer’s rule to solve the linear system.$4x+3y=5\ \ $4x+3y=5 ​$3x+2y=4$3x+2y=4​Solution: (, )

Cramer's rule is a method used to solve systems of linear equations by expressing the solutions in terms of determinants. Here's how you can use it to solve the given system of equations:

The system of equations is:

4x + 3y = 5 3x + 2y = 4

First, we form the coefficient matrix A and the constant matrix B:

A = | 4 3 | | 3 2 |

B = | 5 | | 4 |

Next, we calculate the determinant of A, denoted as |A|:

|A| = (42) - (33) = 8 - 9 = -1

Now, we form two new matrices by replacing each column of A with B, one at a time, and calculate their determinants:

A1 = | 5 3 | | 4 2 |

|A1| = (52) - (43) = 10 - 12 = -2

A2 = | 4 5 | | 3 4 |

|A2| = (44) - (35) = 16 - 15 = 1

Finally, we find the solutions x and y by dividing the determinants of the new matrices by the determinant of A:

x = |A1| / |A| = -2 / -1 = 2 y = |A2| / |A| = 1 / -1 = -1

So, the solution to the system of equations is (2, -1).