# 2019 10th Maths Sample Paper 2019 | Question 12

#### Section B | Linear Equations - Infinitely Many Solutions

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

## NCERT Solution to Class 10 Maths

### Explanatory Answer | CBSE Sample Question Paper 2019 Q12

#### Infinitely Many Solutions

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
$\frac{b1}{b2}$ = $\frac{c1}{c2}$ ⇒ $\frac{3}{p}$ = $\frac{-p}{-12}$
p2 = 36 => p = ± 6

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

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