Use matrices to solve the system of equations. $\left\{ \begin{array} { l }
x + y = 8 \
x - y = 2
\end{array} \right.$
A) (5,3)
B) (4,2)
C) (-5,-3)
D) no solution
E) infinitely many solutions

Question

Use matrices to solve the system of equations. $\left\{ \begin{array} { l } 
x + y = 8 \
x - y = 2
\end{array} \right.$
A) (5,3)
B) (4,2)
C) (-5,-3)
D) no solution
E) infinitely many solutions

Quizplus · Accepted Answer

To solve the system of equations using matrices, we can write 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 = [[1, 1], [1, -1]], X = [[x], [y]], and B = [[8], [2]]. Solving for X gives X = A^(-1)B. Calculating A^(-1) and then multiplying by B gives the solution (5, 3).

Use Matrices to Solve the System of Equations {x+y=8x−y=2\left\{ \begin{array} { l } x + y = 8 \\x - y = 2\end{array} \right.{x+y=8x−y=2​

Use Matrices to Solve the System of Equations $\left\{ \begin{array} { l } x + y = 8 \\x - y = 2\end{array} \right.$