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- x + py = 1 and px - y = 1, if the pair of equations has no solution.Find the value(s) of p the pair of equations

Solution:

Given, the pair of linear equations are

-x + py = 1

px - y = 1

We have to determine the value of p for which the pair of linear equations will have no solution.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then the graph will be a pair of parallel lines and so the pair of equations will have no solution.

Here, a₁ = -1, b₁ = p, c₁ = 1

a₂ = p, b₂ = -1, c₂ = 1

So, a₁/a₂ = -1/p

b₁/b₂ = p/-1 = -p

c₁/c₂ = 1/1 = 1

For no solution,

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)

So, -1/p = -p ≠ 1

Case 1) -1/p = -p

1/p = p

p² = 1

p = ±1

Case 2) -p ≠ 1

p ≠ -1

So, p = +1

Therefore, for the value of p = 1, the pair of linear equations have no solution.

✦ Try This: For which value(s) of λ, do the pair of linear equations λx + 2y = 2λ/3 and x/2 + 5λy = 10 have no solution

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 4 (ii)

- x + py = 1 and px - y = 1, if the pair of equations has no solution.Find the value(s) of p the pair of equations

Summary:

For the value of p = 1, the pair of linear equations -x + py = 1 and px - y = 1 has no solution.

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