Use Cramer's Rule, if possible, to solve the system of linear equations.
-$$\left\{ \begin{array} { r }
- 2 x + 2 y = 16 \
4 x + 4 y = 40
\end{array} \right.$$
A) $( 9,1 )$
B) $( 1,9 )$
C) $( - 9,1 )$
D) $( - 1 , - 9 )$

Question

Use Cramer's Rule, if possible, to solve the system of linear equations.
-$$\left\{ \begin{array} { r } 
- 2 x + 2 y = 16 \
4 x + 4 y = 40
\end{array} \right.$$
A) $( 9,1 )$
B) $( 1,9 )$
C) $( - 9,1 )$
D) $( - 1 , - 9 )$

Quizplus · Accepted Answer

Cramer's Rule can be applied to a system of equations by finding the determinant of the coefficient matrix and the determinants of matrices formed by replacing one column of the coefficient matrix with the constants from the right-hand side of the equations. However, in this case, the system is dependent (the second equation is a multiple of the first), which means Cramer's Rule directly won't give a unique solution. But by solving the system manually, we can find that $x = 1$ and $y = 9$, which corresponds to choice B.

Use Cramer's Rule, If Possible, to Solve the System of Linear