Question

If 2x+3y = 8 and 4x+py=16
, has infinite
solutions, the p=?​

Answer 1

SOLUTION

GIVEN

2x + 3y = 8 and 4x + py = 16 has infinite solutions

TO DETERMINE

The value of p

CONCEPT TO BE IMPLEMENTED

A pair of Straight Lines

$\displaystyle \sf{ a_1x+b_1y+c_1=0 \: \: and \: \: \: a_2x+b_2y+c_2=0}$

is said to have infinite number of solution if

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

EVALUATION

Here the given system of equations are

2x + 3y = 8

4x + py = 16

Now the given equations have infinite number of solutions

$\displaystyle\sf{ \frac{2}{4} = \frac{3}{p} = \frac{8}{16} }$

$\displaystyle\sf{ \implies \: \frac{1}{2} = \frac{3}{p} = \frac{1}{2} }$

$\displaystyle\sf{ \implies \: \frac{3}{p} = \frac{1}{2} }$

$\displaystyle\sf{ \implies \: p = 3 \times 2 }$

$\displaystyle\sf{ \implies \: p = 6 }$

FINAL ANSWER

Hence the required value of p = 6

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