Question

values of p for which the equations have infinitely many solutions px+3=3; 12x+py=6

Answer 1

Correct Question :

Find the value of p for which the equation have infinitely many solution, px + 3y = 3 , 12x + py = 6.

AnsWer :

P = 6.

Concepts Required :

$\tt for \: many \: solution. \\ \tt \: \: \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$

Solution :

We have pair of liner equation,

$\tt px + 3y = 3. \: \: \: \: \: - (1) \\ \tt 12x + py = 6. \: \: \: \: \: - (2)$

Where as,

For A.

• a1 = p.
• a2 = 12.

For B.

• b1 = 3.
• b2 = p.

For C.

• c1 = 3.
• c2 = 6.

Substitute all given value in it, We get.

$\tt \longmapsto \frac{p}{12} = \frac{3}{p} = \frac{3}{6}$

$\tt \longmapsto {p}^{2} = 12 \times 3.$

$\tt \longmapsto {p}^{2} = 36.$

$\tt \longmapsto p = \pm6.$

$\rule{120}1$

And,

$\tt \longmapsto \frac{3}{p} = \frac{3}{6}$

$\tt \longmapsto p = 6.$

Here, We can see, the Solution of above be 6,

$\tt \mapsto \red{p \neq - 6.}$

Negative sign ignore.

Therefore, the solution of given equation be 6.