Choose the one alternative that best completes the statement or answers the question.
Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l }
4 x - 7 y = 5 \
2 x + 5 y = - 3
\end{array} \right.$$
A) $x = - \frac { 2 } { 17 } , y = \frac { 11 } { 17 }$
B) $x = \frac { 23 } { 3 } , y = - \frac { 11 } { 3 }$
C) $x = \frac { 2 } { 17 } , y = - \frac { 11 } { 17 }$
D) $x = \frac { 2 } { 3 } , y = \frac { 1 } { 3 }$

Question

Choose the one alternative that best completes the statement or answers the question.
Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
4 x - 7 y = 5 \
2 x + 5 y = - 3
\end{array} \right.$$
A) $x = - \frac { 2 } { 17 } , y = \frac { 11 } { 17 }$
B) $x = \frac { 23 } { 3 } , y = - \frac { 11 } { 3 }$
C) $x = \frac { 2 } { 17 } , y = - \frac { 11 } { 17 }$
D) $x = \frac { 2 } { 3 } , y = \frac { 1 } { 3 }$

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants. The determinant of the coefficient matrix is 4(5) - (-7)(2) = 20 + 14 = 34. For x, replace the first column with the constants: det = 5(5) - (-3)(-7) = 25 - 21 = 4. For y, replace the second column: det = 4(-3) - 2(5) = -12 - 10 = -22. Thus, x = 4/34 = 2/17 and y = -22/34 = -11/17.

Choose the One Alternative That Best Completes the Statement or Answers