Question

The value of a for which the pair of equation 3x + ay = 6 and 6x + 8y = 7 will
have infinitely many solution is * need only answe​

Answer 1

The two values of a for which the pair of equation 3x + ay = 6 and 6x + 8y = 7 will  have infinitely many solutions is a = 4  and  a = $\frac{48}{7}$.

Step-by-step explanation:

We are given with the two equations below;

3x + ay = 6 and 6x + 8y = 7

Firstly, here

$a_1$ = 3                $a_2$ = 6

$b_1$ = a                 $b_2$ = 8

$c_1$ = 6                 $c_2$ = 7

Now, for eqautions to have infinitely many solutions, the condition for that is ;

                            $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

When this condition holds, then we say that the equation has infinitely many solutions.

So,              $\frac{3}{6}=\frac{a}{8}=\frac{6}{7}$

Firstly take,   $\frac{3}{6}=\frac{a}{8}$

                     a  =  $\frac{3 \times 8}{6}$ = 4

Then take,   $\frac{a}{8}=\frac{6}{7}$

                    a  =  $\frac{6 \times 8}{7}$  = $\frac{48}{7}$

So, the two values of a for which the pair of equation 3x + ay = 6 and 6x + 8y = 7 will  have infinitely many solutions is a = 4  and a = $\frac{48}{7}$.

Answer 2

Answer:

a = 6

Step-by-step explanation:

$3x + ay = 6 \\ 3x + ay - 6 = 0 \\ \\ 6x + 8y = 7 \\ 6x + 8y - 7 = 0$

if eqn. have infinitely many soln. then,

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \\ \frac{3}{6} = \frac{a}{8} = \frac{ - 6}{ - 7} \\ \\ \frac{1}{2} = \frac{a}{8} = \frac{6}{7} \\ \\ 2a = 8 \\ a = \frac{8}{2} \\ a = 4$

Hope this helphul..>_<