Solve using Cramer's rule.
-$$\begin{array} { l }
2 x - 2 y = 2 \
2 x + 3 y = 37
\end{array}$$
A) $( - 7,8 )$
B) $( - 8 , - 7 )$
C) $( 7,8 )$
D) $( 8,7 )$

Question

Solve using Cramer's rule.
-$$\begin{array} { l } 
2 x - 2 y = 2 \
2 x + 3 y = 37
\end{array}$$
A) $( - 7,8 )$
B) $( - 8 , - 7 )$
C) $( 7,8 )$
D) $( 8,7 )$

Quizplus · Accepted Answer

Cramer's rule is used to solve systems of linear equations. The solution is found by calculating the determinants of matrices. For the given system:$$D = \begin{vmatrix} 2 & -2 \ 2 & 3 \end{vmatrix} = (2*3) - (-2*2) = 6 + 4 = 10$$$$D_x = \begin{vmatrix} 2 & -2 \ 37 & 3 \end{vmatrix} = (2*3) - (-2*37) = 6 + 74 = 80$$$$D_y = \begin{vmatrix} 2 & 2 \ 2 & 37 \end{vmatrix} = (2*37) - (2*2) = 74 - 4 = 70$$$$x = \frac{D_x}{D} = \frac{80}{10} = 8$$$$y = \frac{D_y}{D} = \frac{70}{10} = 7$$Therefore, the solution is $x = 8$ and $y = 7$, which corresponds to choice D $(8,7)$.

Solve Using Cramer's Rule 2x−2y=22x+3y=37\begin{array} { l } 2 x - 2 y = 2 \\2 x + 3 y = 37\end{array}2x−2y=22x+3y=37​

Solve Using Cramer's Rule $\begin{array} { l } 2 x - 2 y = 2 \\2 x + 3 y = 37\end{array}$