Answer:
x= 3
y=2
Step-by-step explanation:
-3x + 9y = 9 ----------- equation 1
3x + 2y = 13--------------- equation 2
In Matrix Form
[tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right][/tex]
Let A = [tex]\left[\begin{array}{cc}-3&9\\3&2\end{array}\right][/tex] X = [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] and B = [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Then Mathematically AX= B
or X= A⁻¹ B
Where A⁻¹ = Adjacent A/ mod of A
Adjacent A = [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex]
Mod Of A= -6 - (27) = -33 which is not equal to zero
so Putting These values in the given formula
X= 1/-33 [tex]\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right][/tex] [tex]\left[\begin{array}{c}9\\13\end{array}\right][/tex]
Now Multiplying Rows and Columns
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right][/tex]
Solving the Matrix we get
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right][/tex]
[tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex] = -1/33 [tex]\left[\begin{array}{cc}-99\\-66\end{array}\right][/tex]
From Here we find x= 99/33 or 3
and y = 66/33= 2
