Find the value of a for which the following system of equations has unique solution:
9x + py – 1 = 0, 3x + 4y – 2 = 0

Question

Find the value of a for which the following system of equations has unique solution:9x + py – 1 = 0, 3x + 4y – 2 = 0

Philoid · Accepted Answer

Given, pair of equations

9x + py &ndash; 1 = 0

and 3x + 4y &ndash; 2 = 0

On comparing the given equation with standard form i.e. a1 x + b1y + c1 = 0 and a2 x + b2y + c2 = 0, we get

a1 = 9, b1 = p and c1 = &ndash; 1

and a2 = 3, b2 = 4 and c2 = &ndash; 2

For unique solutions,

Here,

&there4; 3 &ne; p/4   I     II
On taking I and II terms, we get

p &ne; 12

Thus, given lines have a unique solution for all real values of p, except 12.