Solve the system of equations using Cramer's rule.
-$3 x+y=7$
$6 x+4 y=4$
A) $(-5,-4)$
B) $(4,-4)$
C) $(4,-5)$
D) $(-5,4)$

Question

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants. The determinant of the coefficient matrix (D) is $3(4) - 6(1) = 12 - 6 = 6$. For $x$, replace the x-coefficients with the constants to get $D_x = 7(4) - 6(7) = 28 - 42 = -14$, so $x = D_x / D = -14 / 6 = -7/3$. For $y$, replace the y-coefficients with the constants to get $D_y = 3(4) - 7(6) = 12 - 42 = -30$, so $y = D_y / D = -30 / 6 = -5$. However, it seems there was a mistake in my calculation. Let's correct that:For the system:$$3x + y = 7$$$$6x + 4y = 4$$The determinant (D) of the coefficient matrix is calculated as:$$D = (3)(4) - (1)(6) = 12 - 6 = 6$$For $x$, we find the determinant $D_x$ by replacing the x-coefficients with the constants from the equations:$$D_x = \begin{vmatrix} 7 & 1 \ 4 & 4 \end{vmatrix} = (7)(4) - (1)(4) = 28 - 4 = 24$$Thus, $x = D_x / D = 24 / 6 = 4$.For $y$, we find the determinant $D_y$ by replacing the y-coefficients with the constants:$$D_y = \begin{vmatrix} 3 & 7 \ 6 & 4 \end{vmatrix} = (3)(4) - (7)(6) = 12 - 42 = -30$$Thus, $y = D_y / D = -30 / 6 = -5$.Therefore, the correct solution is $x = 4$, $y = -5$, which matches choice C.

Solve the System of Equations Using Cramer's Rule 3x+y=73 x+y=73x+y=7 6x+4y=46 x+4 y=46x+4y=4

Solve the System of Equations Using Cramer's Rule $3 x+y=7$ $6 x+4 y=4$