Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { c }
x + 3 y = - 12 \
4 x + 4 y = - 16
\end{array}$$
A) $\{ ( 0 , - 4 ) \}$
B) $\{ ( 4,0 ) \}$
C) $\{ ( 1 , - 5 ) \}$
D) Cramer's rule does not apply since $D = 0 ; \varnothing$

Question

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { c } 
x + 3 y = - 12 \
4 x + 4 y = - 16
\end{array}$$
A) $\{ ( 0 , - 4 ) \}$
B) $\{ ( 4,0 ) \}$
C) $\{ ( 1 , - 5 ) \}$
D) Cramer's rule does not apply since $D = 0 ; \varnothing$

Quizplus · Accepted Answer

First, find the determinant $D$ of the coefficient matrix. Here, $D = (1)(4) - (3)(4) = 4 - 12 = -8$, which is not zero, so Cramer's rule applies. Solving using Cramer's rule or another method gives the solution $(0, -4)$.

Use Cramer's Rule to Solve the System of Equations x+3y=−124x+4y=−16\begin{array} { c } x + 3 y = - 12 \\4 x + 4 y = - 16\end{array}x+3y=−124x+4y=−16​

Use Cramer's Rule to Solve the System of Equations $\begin{array} { c } x + 3 y = - 12 \\4 x + 4 y = - 16\end{array}$