 # 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 29 Pair of Linear Equations in Two Variables - Exercise 3.3

2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution. Find p.

Given, pair of linear equations is

2x + 3y – 5 = 0

px – 6y – 8 = 0

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

Here, a1 = 2, b1 = 3, c1 = – 5;

And a2 = p, b2 = – 6, c2 = – 8;

a1 /a2 = 2/p

b1 /b2 = – 3/6 = – ½

c1 /c2 = 5/8

Since, the pair of linear equations has a unique solution.

a1/a2 ≠ b1/b2

so 2/p ≠ – ½

p ≠ – 4

Hence, the pair of linear equations has a unique solution for all values of p except – 4.

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