Solve using Cramer's rule.
-2x - 2y = 2 2x + 3y = 37
A) (-7, 8)
B) (-8, -7)
C) (7, 8)
D) (8, 7)

Question

Quizplus · Accepted Answer

Cramer's rule involves using determinants to solve a system of linear equations. For the given system:1. The determinant of the coefficient matrix (D) is calculated using the coefficients of x and y:$$D = \begin{vmatrix} 2 & -2 \ 2 & 3 \end{vmatrix} = (2*3) - (2*(-2)) = 6 + 4 = 10.$$2. The determinant for x (Dx) replaces the x coefficients with the constants from the equations:$$D_x = \begin{vmatrix} 2 & -2 \ 37 & 3 \end{vmatrix} = (2*3) - (37*(-2)) = 6 + 74 = 80.$$3. The determinant for y (Dy) replaces the y coefficients with the constants:$$D_y = \begin{vmatrix} 2 & 2 \ 2 & 37 \end{vmatrix} = (2*37) - (2*2) = 74 - 4 = 70.$$4. Solve for x and y:$$x = \frac{D_x}{D} = \frac{80}{10} = 8,$$$$y = \frac{D_y}{D} = \frac{70}{10} = 7.$$Therefore, the solution is (8, 7).

Solve Using Cramer's Rule