Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l }
3 x + 3 y = 51 \
2 x - 2 y = 2
\end{array} \right.$$
A) x = 8, y = 9
B) x = 9, y = 8
C) x = -9, y = -8
D) x = -8, y = 9

Question

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
3 x + 3 y = 51 \
2 x - 2 y = 2
\end{array} \right.$$
A) x = 8, y = 9
B) x = 9, y = 8
C) x = -9, y = -8
D) x = -8, y = 9

Quizplus · Accepted Answer

To solve the system using Cramer's rule, we first find the determinant of the coefficient matrix, $\Delta$, and then the determinants of matrices formed by replacing the columns of the coefficient matrix with the constants on the right-hand side ($\Delta_x$ and $\Delta_y$). The system is:$$3x + 3y = 51$$$$2x - 2y = 2$$The coefficient matrix and its determinant ($\Delta$) are:$$\begin{vmatrix}3 & 3 \2 & -2\end{vmatrix} = (3)(-2) - (3)(2) = -6 - 6 = -12$$For $\Delta_x$ (replacing x's coefficients with the constants):$$\begin{vmatrix}51 & 3 \2 & -2\end{vmatrix} = (51)(-2) - (3)(2) = -102 - 6 = -108$$For $\Delta_y$ (replacing y's coefficients with the constants):$$\begin{vmatrix}3 & 51 \2 & 2\end{vmatrix} = (3)(2) - (51)(2) = 6 - 102 = -96$$Solving for $x$ and $y$:$$x = \frac{\Delta_x}{\Delta} = \frac{-108}{-12} = 9$$$$y = \frac{\Delta_y}{\Delta} = \frac{-96}{-12} = 8$$Therefore, $x = 9$ and $y = 8$, which corresponds to choice B.

Use Cramer's Rule to Solve the Linear System {3x+3y=512x−2y=2\left\{ \begin{array} { l } 3 x + 3 y = 51 \\2 x - 2 y = 2\end{array} \right.{3x+3y=512x−2y=2​

Use Cramer's Rule to Solve the Linear System $\left\{ \begin{array} { l } 3 x + 3 y = 51 \\2 x - 2 y = 2\end{array} \right.$