Question

if 3x - y = 7, ax + 4y = 11 and dy=26 then a = ?​

Answer 1

Given:

Given equations are, 3x - y = 7

                                   ax + 4y = 11

To find:

the value of a

Solution:

Equation(1) is given -

3x - y = 7

a₁ = 3

 b₁ = -1

 c₁ = 7

Equation(2) is given -

ax + 4y = 11

 a₂ = a

 b₂ = 4

 c₂ = 11

then,

$D = \begin{vmatrix}a_1 & b_1\\ a_2& b_2\end{vmatrix}$

$D = \begin{vmatrix}3 & -1\\ 1& 4\end{vmatrix}$

D = (3 × 4) - (-1 × 1) = 12+1 = 13

and

$D_x = \begin{vmatrix}c_1 & b_1\\ c_2& b_2\end{vmatrix}$

$D_x = \begin{vmatrix}7 & -1\\ 11& 4\end{vmatrix}$

$D_x$ = (7 × 4) - (-1 × 11) = 28 + 11

$D_x$ = 39

also,

$D_y = \begin{vmatrix}a_1 & c_1\\ a_2& c_2\end{vmatrix}$

$D_y = \begin{vmatrix}3 & 7\\ 1& 11\end{vmatrix}$

$D_y$ = (3 × 11) - (7 × 1) = 33-7

$D_y$ = 26

by using Cramer's rule, we have

  $x = \frac{D_x}{D} = \frac{39}{13}$

x = 3

$y = \frac{D_y}{D} = \frac{26}{13}$

y = 2

so, by putting values of x and y in equation (2), we will get the value of a which is,

  a × 3 + 4 × 2 = 11

   3a + 8 = 11

   3a = 11-8

    3a = 3

    a = 1

Hence, the value of a is 1.

Answer 2

Given :  3x - y = 7

ax + 4y = 11

Dy =  26

To Find :  Value of a

Solution:

Using Cramer rule :

x = Dₓ/D

y = Dy/D

3x  -  y = 7

ax + 4y = 11

$D=\left|\begin{array}{ccc}3&-1\\a&4\end{array}\right|$

$D_x=\left|\begin{array}{ccc}7&-1\\11&4\end{array}\right|$

$D_y=\left|\begin{array}{ccc}3&7\\a&11\end{array}\right|$

=> 3 * 11  - 7a = 26

=> -7a = -7

=> a = 1

Hence value of a = 1

on Solving x = 3 and y = 2

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