Use Cramer s Rule to solve the system $\left\{ \begin{array} { l }
2 x - 3 y = 7 \
x - 5 y = 7
\end{array} \right.$
A) no solution; inconsistent system
B) infinitely many solutions; dependent equations
C) (2,-1)
D) (-2,1)

Question

Use Cramer s Rule to solve the system $\left\{ \begin{array} { l } 
2 x - 3 y = 7 \
x - 5 y = 7
\end{array} \right.$
A) no solution; inconsistent system
B) infinitely many solutions; dependent equations
C) (2,-1)
D) (-2,1)

Quizplus · Accepted Answer

Using Cramer's Rule, we set up the determinant:
$$\begin{vmatrix}2&-3\1&-5\end{vmatrix}=2(-5)-(-3)(1)=-10+3=-7$$
Then we set up the determinant for $x$:
$$\begin{vmatrix}7&-3\7&-5\end{vmatrix}=7(-5)-(-3)(7)=-35+21=-14$$
So $x=\frac{-14}{-7}=2$.
Next, we set up the determinant for $y$:
$$\begin{vmatrix}2&7\1&7\end{vmatrix}=2(7)-(1)(7)=14-7=7$$
So $y=\frac{7}{-7}=-1$.
Therefore, the unique solution is $(x,y)=(2,-1)$, so the answer is C.

Use Cramer S Rule to Solve the System {2x−3y=7x−5y=7\left\{ \begin{array} { l } 2 x - 3 y = 7 \\x - 5 y = 7\end{array} \right.{2x−3y=7x−5y=7​

Use Cramer S Rule to Solve the System $\left\{ \begin{array} { l } 2 x - 3 y = 7 \\x - 5 y = 7\end{array} \right.$