Use Cramer's Rule to solve (if possible) the system of equations. $$\left\{ \begin{array} { l }
4 x - 3 y = - 30 \
6 x + 9 y = - 18
\end{array} \right.$$
A)(-6, 2)
B)(6, -2)
C)(6, 2)
D)(2, -6)
E)(-6, -2)

Question

Use Cramer's Rule to solve (if possible) the system of equations.   $$\left\{ \begin{array} { l } 
4 x - 3 y = - 30 \
6 x + 9 y = - 18
\end{array} \right.$$  
A)(-6, 2)
B)(6, -2)
C)(6, 2)
D)(2, -6)
E)(-6, -2)

Quizplus · Accepted Answer

Cramer's Rule involves using determinants to solve a system of equations. For the given system, the determinant of the coefficient matrix is $D = 4(9) - (-3)(6) = 36 + 18 = 54$. For $x$, replace the x-coefficients with the constants to get $D_x = (-30)(9) - (-18)(-3) = -270 - 54 = -324$, so $x = D_x / D = -324 / 54 = -6$. For $y$, replace the y-coefficients with the constants to get $D_y = 4(-18) - (-30)(6) = -72 + 180 = 108$, so $y = D_y / D = 108 / 54 = 2$. Thus, the solution is $(-6, 2)$.

Use Cramer's Rule to Solve (If Possible) the System of Equations