 # NCERT Exemplar Solutions Class 10 Mathematics Solutions for Pair of Linear Equations in Two Variables - Exercise 3.3 in Chapter 3 - Pair of Linear Equations in Two Variables

Question 31 Pair of Linear Equations in Two Variables - Exercise 3.3

– 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point. Find p.

Given, pair of linear equations is

– 3x + 5y = 7

2px – 3y = 1

On comparing with ax + by + c = 0, we get

Here, a1 = -3, b1 = 5, c1 = – 7;

And a2 = 2p, b2 = – 3, c2 = – 1;

a1 /a2 = -3/ 2p

b1 /b2 = – 5/3

c1 /c2 = 7

Since, the lines are intersecting at a unique point i.e., it has a unique solution

a1/a2 ≠ b1/b2

-3/2p ≠ -5/3

p ≠ 9/10

Hence, the lines represented by these equations are intersecting at a unique point for all real values of p except 9/10

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