Question

If the lines given by ax–y=3 and 21x−3y=9 will have infinitely many solutions ,then the
value of ais

Answer 1

Answer:

a=7

Step-by-step explanation:

a/21=3/9=a/21=1/3

a=21/3

a=7

Answer 2

Linear equations

The given equations are

$\quad\quad ax-y=3$

$\quad\quad 21x-3y=9$

For infinitely many solutions, we must have

$\quad\frac{a}{21}=\frac{-1}{-3}$

$\Rightarrow \frac{a}{21}=\frac{1}{3}$

$\Rightarrow a=\frac{21}{3}$

$\Rightarrow a=7$

Answer. The value of a is 7.

Remark. Geometrical approach

The given linear equations will have infinitely many solutions when they are identical.

The second line has coefficient $(-3)$ of $y$. Multiplying $3$ to both sides of the equation of the first line, we get the coefficient of $x$ being $3a$.

So, $3a=21$

$\Rightarrow a=7$