Question

9, 4x-3y = 33x-5y = 71

Answer 1

The given system of equations is,

4x−3y=3

3x−5y=7

Write the system of equations in the form of AX=B.

[ 4 −3 3 −5 ][ x y ]=[ 3 7 ]

Now, the determinant of A is,

| A |=−20+9 =−11

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 = adjA | A |

The value of adjA is,

adjA=[ −5 3 −3 4 ]

Since | A |=−11, thus,

A −1 = −1 11 [ −5 3 −3 4 ]

Now,

X= A −1 B [ x y ]= −1 11 [ −5 3 −3 4 ][ 3 7 ] [ x y ]= −1 11 [ −15+21 −9+28 ] [ x y ]= −1 11 [ 6 19 ]

Hence,

[ x y ]=[ −6 11 −19 11 ]

Thus x= −6 11 and y= −19 11 .