Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l }
x + y = - 6 \
x - y = 2
\end{array} \right.$$
A) $( - 2 , - 4 )$
B) $( - 4 , - 2 )$
C) $( - 2,4 )$
D) $\varnothing$

Question

Solve the system of linear equations using matrices.
-$$\left\{ \begin{array} { l } 
x + y = - 6 \
x - y = 2
\end{array} \right.$$
A) $( - 2 , - 4 )$
B) $( - 4 , - 2 )$
C) $( - 2,4 )$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system of equations using matrices, we can represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix. For the given system:$$A = \begin{pmatrix} 1 & 1 \ 1 & -1 \end{pmatrix}, X = \begin{pmatrix} x \ y \end{pmatrix}, B = \begin{pmatrix} -6 \ 2 \end{pmatrix}$$To find X, we calculate $A^{-1}B$:$$A^{-1} = \frac{1}{(1)(-1) - (1)(1)} \begin{pmatrix} -1 & -1 \ -1 & 1 \end{pmatrix} = \frac{1}{-2} \begin{pmatrix} -1 & -1 \ -1 & 1 \end{pmatrix} = \begin{pmatrix} 0.5 & 0.5 \ 0.5 & -0.5 \end{pmatrix}$$$$X = A^{-1}B = \begin{pmatrix} 0.5 & 0.5 \ 0.5 & -0.5 \end{pmatrix} \begin{pmatrix} -6 \ 2 \end{pmatrix} = \begin{pmatrix} -2 \ -4 \end{pmatrix}$$Therefore, the solution to the system of equations is $x = -2, y = -4$, which corresponds to choice A $(-2, -4)$.

Solve the System of Linear Equations Using Matrices {x+y=−6x−y=2\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.{x+y=−6x−y=2​

Solve the System of Linear Equations Using Matrices $\left\{ \begin{array} { l } x + y = - 6 \\x - y = 2\end{array} \right.$