10. 5x+2y 33x 2y 5
The given system of equations is,
5 x + 2 y = 3
3 x + 2 y = 5
Write the system of equations in the form of AX = B .
[ 5 2 3 2 ] [ x y ] = [ 3 5 ]
Now, the determinant of A is,
| A | = 10 − 6 = 4
Since | A | ≠ 0 , thus A is non-singular, therefore, its inverse exists.
Since AX = B , thus, X = A -1 B .
It is known that,
A − 1 = a d j A | A |
The value of a d j A is,
a d j A = [ 2 − 2 − 3 5 ]
Since | A | = 4 , thus,
A − 1 = 1 4 [ 2 − 2 − 3 5 ]
Now,
X = A − 1 B [ x y ] = 1 4 [ 2 − 2 − 3 5 ] [ 3 5 ] [ x y ] = 1 4 [ 6 − 10 − 9 + 25 ] [ x y ] = 1 4 [ − 4 16 ]
Hence,
[ x y ] = [ − 1 4 ]
Thus x = − 1 and y = 4 .
The given system of equations is,
Write the system of equations in the form of
Now, the determinant of
Since
Since
It is known that,
The value of
Since
Now,
Hence,
Thus
