Answer:
(x,y)=(-11,2)
Step-by-step explanation:
x+2y=-7, -3x-5y=23; Matrix form:[tex]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][/tex]; Finally (x,y) = (-11,2)
Answer:
Solve the system of equations using elimination/combination method. State your answer as an ordered pair.
{x,y} = {-11,2}
Step-by-step 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}
