Use matrices to solve the system of equations. $\left\{ \begin{array} { l }
3 x + y = 11 \
x + 3 y = - 7
\end{array} \right.$
A) (5,-4)
B) (6,-30
C) (-5,4)
D) no solution
E) infinitely many solutions

Question

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 
3 x + y = 11 \
x + 3 y = - 7
\end{array} \right.$
A) (5,-4)
B) (6,-30
C) (-5,4)
D) no solution
E) infinitely many solutions

Quizplus · Accepted Answer

We write the system of equations in matrix form as $ \left(\begin{array}{cc} 3 & 1 \ 1 & 3 \\end{array}ight) \left(\begin{array}{c} x \ y \\end{array}ight) = \left(\begin{array}{c} 11 \ -7 \\end{array}ight)$. Then taking the inverse of the coefficient matrix, we have $\left(\begin{array}{c} x \ y \\end{array}ight) = \left(\begin{array}{cc} 3 & 1 \ 1 & 3 \\end{array}ight)^{-1} \left(\begin{array}{c} 11 \ -7 \\end{array}ight) = \dfrac{1}{8} \left(\begin{array}{cc} 3 & -1 \ -1 & 3 \\end{array}ight) \left(\begin{array}{c} 11 \ -7 \\end{array}ight) = \left(\begin{array}{c} 5 \ -4 \\end{array}ight).$ Thus the solution is $(x,y) = \boxed{	extbf{(A)}\ (5,-4)}$.

Use Matrices to Solve the System of Equations {3x+y=11x+3y=−7\left\{ \begin{array} { l } 3 x + y = 11 \\x + 3 y = - 7\end{array} \right.{3x+y=11x+3y=−7​

Use Matrices to Solve the System of Equations $\left\{ \begin{array} { l } 3 x + y = 11 \\x + 3 y = - 7\end{array} \right.$