Use Cramer's Rule, if possible, to solve the system of linear equations.
-$\left\{ \begin{array} { c } 2 x + 2 y = 16 \ 2 x - 2 y = - 8 \ \end{array} \right.$

A) $( - 2 , - 6 )$
B) $( 6,2 )$
C) $( 2,6 )$
D) $( - 6,2 )$

Question

Use Cramer's Rule, if possible, to solve the system of linear equations.
-$\left\{ \begin{array} { c } 2 x + 2 y = 16 \ 2 x - 2 y = - 8 \  \end{array} \right.$

A) $( - 2 , - 6 )$ 
B) $( 6,2 )$
C) $( 2,6 )$
D) $( - 6,2 )$

Quizplus · Accepted Answer

Cramer's Rule can be used to solve a system of linear equations when there is the same number of equations as unknowns, and the determinant of the coefficient matrix is not zero. For the given system:$$\begin{align*}2x + 2y &= 16 \2x - 2y &= -8\end{align*}$$The coefficient matrix is $\begin{pmatrix} 2 & 2 \ 2 & -2 \end{pmatrix}$, and its determinant is $(-2)(2) - (2)(2) = -8$, which is not zero, so Cramer's Rule applies.To find $x$, replace the first column of the coefficient matrix with the constants to get $\begin{pmatrix} 16 & 2 \ -8 & -2 \end{pmatrix}$, whose determinant is $(-2)(16) - (2)(-8) = -32 + 16 = -16$. Dividing by the determinant of the coefficient matrix gives $x = \frac{-16}{-8} = 2$.To find $y$, replace the second column of the coefficient matrix with the constants to get $\begin{pmatrix} 2 & 16 \ 2 & -8 \end{pmatrix}$, whose determinant is $(2)(-8) - (2)(16) = -16 - 32 = -48$. Dividing by the determinant of the coefficient matrix gives $y = \frac{-48}{-8} = 6$.Therefore, the solution is $(2, 6)$.

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