For what value of P the following pair of linear equations in two variables will have infinitely many solutions PX 3y p 3 0 12x py p 0 A 6 B 6 C 0 D 2?

This 2019 CBSE class 10 Maths 2 mark question is from Linear Equations. An easy 2 mark question in CBSE class 10 sample question paper. A standard NCERT text book question.

Question 12: For what value of p will the following pair of linear equations have infinitely many solutions: (p - 3)x + 3y = p and px + py = 12

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For two equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
Condition for infinitely many solutions => \\frac{a_1}{a_2}) = \\frac{b_1}{b_2}) = \\frac{c_1}{c_2})

The given equations are (p - 3)x + 3y - p = 0 and px + py – 12 = 0
\\frac{a_1}{a_2}) = \\frac{b_1}{b_2}) ⇒ \\frac{p - 3}{p}) = \\frac{3}{p})
p2 – 3p = 3p ⇒ p2 – 6p = 0 p(p – 6) = 0 ⇒ p = 0 or 6

\\frac{b1}{b2}) = \\frac{c1}{c2}) ⇒ \\frac{3}{p}) = \\frac{-p}{-12})

The only value that satisfies both the ratios is +6. The value of p is 6.