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Pair of Linear Equations in Two Variables | Pair of Linear Equations in Two Variables - Exercise 3.3

Question 14

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

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Given pair of linear equations is

– x + py = 1 …(i)

px – y – 1 = 0 …(ii)

On comparing with ax + by + c = 0,

We get,

a1 = -1, b1 = p, c1 =- 1;

a2 = p, b2 = – 1, c2 =- 1;

a1 /a2 = -1/p

b1 /b2 = – p

c1 /c2 = 1

Since, the lines equations has no solution i.e., both lines are parallel to each other.

a1/a2 = b1/b2≠ c1/c2

-1/p = – p ≠ 1

Taking last two parts, we get

p ≠ -1

Taking first two parts, we get

p2 = 1

p = + 1

Hence, the given pair of linear equations has no solution for p = 1.

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Our top 5% students will be awarded a special scholarship to Lido.

subject-cta

Question 14

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

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Given pair of linear equations is

– x + py = 1 …(i)

px – y – 1 = 0 …(ii)

On comparing with ax + by + c = 0,

We get,

a1 = -1, b1 = p, c1 =- 1;

a2 = p, b2 = – 1, c2 =- 1;

a1 /a2 = -1/p

b1 /b2 = – p

c1 /c2 = 1

Since, the lines equations has no solution i.e., both lines are parallel to each other.

a1/a2 = b1/b2≠ c1/c2

-1/p = – p ≠ 1

Taking last two parts, we get

p ≠ -1

Taking first two parts, we get

p2 = 1

p = + 1

Hence, the given pair of linear equations has no solution for p = 1.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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