Use Cramer's Rule, if possible, to solve the system of linear equations.
-$$\left\{ \begin{array} { l }
x + y = 7 \
6 x + 6 y = 42
\end{array} \right.$$
A) $( 2,5 )$
B) $( 0,0 )$
C) $\{ ( x , y ) \mid x + y = 7 \}$
D) $\varnothing$

Question

Use Cramer's Rule, if possible, to solve the system of linear equations.
-$$\left\{ \begin{array} { l } 
x + y = 7 \
6 x + 6 y = 42
\end{array} \right.$$
A) $( 2,5 )$
B) $( 0,0 )$
C) $\{ ( x , y ) \mid x + y = 7 \}$
D) $\varnothing$

Quizplus · Accepted Answer

Cramer's Rule is applicable only to systems of linear equations where the coefficient matrix is square and has a non-zero determinant. In this case, however, the second equation is a multiple of the first (6x + 6y = 42 is the same as x + y = 7 when both sides of the second equation are divided by 6), indicating that the system has infinitely many solutions that satisfy x + y = 7. This means the system does not have a unique solution, making Cramer's Rule inapplicable for finding a unique solution. Instead, the solution set is all pairs $(x, y)$ that satisfy the equation x + y = 7, which is option C.

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