Question

Solve the system of equations by forming a matrix equation. State your answer as an ordered pair.

Answer 1

Answer:

(x,y)=(-11,2)

Step-by-step explanation:

x+2y=-7, -3x-5y=23; Matrix form:$A\left[\begin{array}{ccc}1&2\\-3&-5\end{array}\right] .X\left[\begin{array}{ccc}x\\y\end{array}\right] =B\left[\begin{array}{ccc}-7\\23\end{array}\right]; X=A^-1.B; If A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] ; so\\ \\A^-1 =(1/(ad-bc))*\left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]; A^-1 =(1/-5+6)*\left[\begin{array}{ccc}-5&-2\\3&1\end{array}\right]=\left[\begin{array}{ccc}-5&-2\\3&1\end{array}\right] , we have: [tex]\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}-5&-2\\3&-1\end{array}\right] .\left[\begin{array}{ccc}-7\\23\end{array}\right]=\left[\begin{array}{ccc}-11\\2\end{array}\right]$; Finally   (x,y) = (-11,2)