Question

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

x+2y= -7
-3x-5y=23

Answer 1

Solve the system of equations using elimination/combination method. State your answer as an ordered pair.

{x,y} = {-11,2}

Explanation:

Solve equation [1] for the variable x

[1] x = -2y - 7

Plug this in for variable x in equation [2]

[2] -3•(-2y-7) - 5y = 23

[2] y = 2

Solve equation [2] for the variable y

[2] y = 2

By now we know this much :

x = -2y-7

y = 2

Use the y value to solve for x

x = -2(2)-7 = -11

{x,y} = {-11,2}

Answer 2

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

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)