find the values of p and q so that the pair of linear equations (2p-1)x+3y-5=0 and 3x+(q-1)y-15=0 has infinite no. of solutions
Answers
the pair of linear equations ; (2p - 1)x + 3y - 5 = 0 and 3x + (q - 1)y - 15 = 0 has infinite no of solutions.
To find : The values of p and q.
solution : concept : the system of two linear equations ; a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0, has infinite no of solutions only if
a₁/a₂ = b₁/b₂ = c₁/c₂
here (2p - 1)x + 3y - 5 = 0
3x + (q - 1)y - 15 = 0
⇒(2p - 1)/3 = 3/(q - 1) = -5/-15
⇒(2p - 1)/3 = 3/(q - 1) = 1/3
case 1 : (2p - 1)/3 = 1/3
⇒2p - 1 = 1
⇒p = 1
case 2 : 3/(q - 1) = 1/3
⇒9 = q - 1
⇒q = 10
Therefore the values of p and q are 1 and 10 respectively.
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Answer:
Step-by-step explanation:
(2p-1)x+3y-5=0 and 3x+(q-1)y-15=0