Question

For what value of 'p' the following pair of equations has a unique solution.2x + py = - 5 and 3x + 3y = - 6

Answer 1

Given :  2x + py = - 5 …………(1)

3x + 3y = - 6……….(2)

The given equation can be written as :

2x + py + 5 = 0

3x + 3y + 6 = 0  On comparing with  a1x + b1y +c1 = 0 &

a2x + b2y + c2 = 0  a1= 2 , b1= p , c1= 5

a2= 3 , b2= 3  , c2 = 6  A pair of linear equations has unique solution,if

a1/a2 ≠ b1/b2

2/3 ≠ p/3

3p ≠ 6

p ≠ 2  Hence, given lines have unique solution for all real values of p except 2.  HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Dear student ,

Answer: p ≠ 2 and p ≠ 5/2

Solution: standard linear equation in two variable is given as a1 x+ b1 y + c 1 = 0

a2 x+ b2 y + c 2= 0

for equation have unique solution,
a1/a2 ≠ b1/b2 ≠ c1/c2

2x + py +5 =0
and 3x + 3y + 6=0

a1 = 2, b1 = p, c1 = 5
a2 = 3, b2 = 3, c2 = 6

2/3 ≠ p/3 ≠5/6

on solving first two ,we get that p ≠ 2

on solving last two conditions we get that p ≠ 5/2.

Hope it helps you.