Use Cramer’s Rule to solve the linear system.$2x+5y=11$2x+5y=11​$4x+8y=20$4x+8y=20​Solution: (, )

Cramer's Rule is a method used to solve systems of linear equations by finding the ratio of determinants. Here's how you can use it to solve the given system of equations:

The system of equations is:

2x + 5y = 11 4x + 8y = 20

First, we form the coefficient matrix A and calculate its determinant:

A = | 2 5 | | 4 8 |

det(A) = 28 - 54 = 16 - 20 = -4

Next, we form a matrix A1 by replacing the first column of A with the column vector of the right-hand side of the equations, and calculate its determinant:

A1 = | 11 5 | | 20 8 |

det(A1) = 118 - 520 = 88 - 100 = -12

Then, we form a matrix A2 by replacing the second column of A with the column vector of the right-hand side of the equations, and calculate its determinant:

A2 = | 2 11 | | 4 20 |

det(A2) = 220 - 114 = 40 - 44 = -4

Finally, we find the solutions x and y by dividing the determinants of A1 and A2 by the determinant of A:

x = det(A1) / det(A) = -12 / -4 = 3 y = det(A2) / det(A) = -4 / -4 = 1

So, the solution to the system of equations is (3, 1).