For Exercises 11–22, use Cramer's Rule to solve each system. 3x - 4y = 42x + 2y = 12

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, using determinants. It states that if the system can be represented in matrix form, the solution for each variable can be found by taking the ratio of the determinant of a modified matrix (where one column is replaced by the constants from the equations) to the determinant of the coefficient matrix.

A determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties of the matrix, such as whether it is invertible. For a 2x2 matrix, the determinant is calculated as ad - bc, where the matrix is represented as [[a, b], [c, d]]. Determinants are crucial in Cramer's Rule for determining the solutions of the variables in a system of equations.

A system of linear equations consists of two or more linear equations involving the same set of variables. The solution to the system is the set of values that satisfy all equations simultaneously. In this case, the system includes two equations with two variables (x and y), and the goal is to find the values of x and y that make both equations true.