Question

To solve x+y=3 ; 3x-2y-4=0 by determinant method find D.
(A) 5
(B) 1
(C) -5
(D) -1

Answer 1

The value of this determinant is found by finding the difference between the diagonally down product and the diagonally up product

now here, the equation is.
x + y = 3
3x - 2y = 4

The denominator determinant, D, is formed by taking the coefficients of x and y from the equations written in standard form.

D = $\left[\begin{array}{cc}1&1\\3&-2\end{array}\right]$
according to formula,
D = ( 1 ) × ( -2 ) - ( 1 ) × ( 3 )
D = - 2 - 3
D = -5
HENCE, option (C) is correct.

Answer 2

Determinant method (Cramer’s Rule) :
In Cramer’s method, the equations are written as a1x + b1y = c1 & a2x + b2y = c2.

The value of determinant :
D = |a1 b1|
       |a2 b2|

D = a1b2 - a2b1

SOLUTION :
Option C is Correct : -5

GIVEN :
x + y = 3 , 3x - 2y - 4=0

Write the equations as a1x + b1y = c1 & a2x + b2y = c2.
x + y = 3 , 3x - 2y = 4

Here, a1= 1,b1= 1,c1= 3
a2 = 3, b²= - 2 , c2 = 4

The value of determinant :
D = |a1 b1|
       |a2 b2|

D = |1 1 |
       |3 -2|

D = a1b2 - a2b1

D = (1×-2) - ( 3×1)
D = -2 -3 = -5

Hence , the value of D is - 5.

HOPE THIS WILL HELP YOU…