Solve a System of Linear Equations in Two Variables Using Cramer's Rule
-$$\begin{array} { l }
2 x + 3 y = 24 \
2 x - 3 y = 12
\end{array}$$
A) $\{ ( 9,2 ) \}$
B) $\{ ( 2,9 ) \}$
C) $\{ ( - 2,9 ) \}$
D) $\{ ( - 9 , - 2 ) \}$

Question

Solve a System of Linear Equations in Two Variables Using Cramer's Rule
-$$\begin{array} { l } 
2 x + 3 y = 24 \
2 x - 3 y = 12
\end{array}$$
A) $\{ ( 9,2 ) \}$
B) $\{ ( 2,9 ) \}$
C) $\{ ( - 2,9 ) \}$
D) $\{ ( - 9 , - 2 ) \}$

Quizplus · Accepted Answer

Cramer's Rule uses determinants to solve a system of linear equations. For the given system, the determinant $D$ of the coefficient matrix is $2(-3) - 2(3) = -12$. The determinant $D_x$ for $x$ is obtained by replacing the $x$-coefficients with the constants (24 and 12), so $D_x = 24(-3) - 12(3) = -72 - 36 = -108$. The determinant $D_y$ for $y$ is obtained by replacing the $y$-coefficients with the constants, so $D_y = 2(12) - 2(24) = 24 - 48 = -24$. Thus, $x = D_x / D = -108 / -12 = 9$ and $y = D_y / D = -24 / -12 = 2$, making the solution $\{(9,2)\}$.

Solve a System of Linear Equations in Two Variables Using 2x+3y=242x−3y=12\begin{array} { l } 2 x + 3 y = 24 \\2 x - 3 y = 12\end{array}2x+3y=242x−3y=12​

Solve a System of Linear Equations in Two Variables Using $\begin{array} { l } 2 x + 3 y = 24 \\2 x - 3 y = 12\end{array}$