Use Cramer's rule to solve the linear system.
-$$\begin{array} { l }
2 x + 2 y = 2 \
3 x + y = - 3
\end{array}$$
A) $( 2 , - 3 )$
B) $( 3 , - 2 )$
C) $( - 2,3 )$
D) $( - 3 , - 2 )$

Question

Use Cramer's rule to solve the linear system.
-$$\begin{array} { l } 
2 x + 2 y = 2 \
3 x + y = - 3
\end{array}$$
A) $( 2 , - 3 )$
B) $( 3 , - 2 )$
C) $( - 2,3 )$
D) $( - 3 , - 2 )$

Quizplus · Accepted Answer

Cramer's rule uses determinants to solve a system of linear equations. For the given system:$$2x + 2y = 2$$$$3x + y = -3$$The determinant of the coefficient matrix (D) is:$$D = \begin{vmatrix} 2 & 2 \ 3 & 1 \end{vmatrix} = (2)(1) - (2)(3) = 2 - 6 = -4$$The determinant for $x$ (Dx) is obtained by replacing the x-coefficients with the constants from the equations:$$D_x = \begin{vmatrix} 2 & 2 \ -3 & 1 \end{vmatrix} = (2)(1) - (2)(-3) = 2 + 6 = 8$$The determinant for $y$ (Dy) is obtained by replacing the y-coefficients with the constants:$$D_y = \begin{vmatrix} 2 & 2 \ 3 & -3 \end{vmatrix} = (2)(-3) - (2)(3) = -6 - 6 = -12$$Solving for $x$ and $y$:$$x = \frac{D_x}{D} = \frac{8}{-4} = -2$$$$y = \frac{D_y}{D} = \frac{-12}{-4} = 3$$Therefore, the solution is $(-2, 3)$.

Use Cramer's Rule to Solve the Linear System 2x+2y=23x+y=−3\begin{array} { l } 2 x + 2 y = 2 \\3 x + y = - 3\end{array}2x+2y=23x+y=−3​

Use Cramer's Rule to Solve the Linear System $\begin{array} { l } 2 x + 2 y = 2 \\3 x + y = - 3\end{array}$