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3x - y - 5 = 0 and 6x - 2y - p = 0, if the lines represented by these equations are parallel. Find the value(s) of p the pair of equations

Solution:

Given, the pair of linear equations are

3x - y - 5 = 0

6x - 2y - p = 0

We have to determine the value of p for which the lines represented by these equations are parallel.

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

i) The pair of linear equation is inconsistent

ii) The graph will be a pair of parallel lines and so the pair of equations will have no solution.

Here, a₁ = 3, b₁ = -1, c₁ = -5

a₂ = 6, b₂ = -2, c₂ = -p

So, a₁/a₂ = 3/6 = 1/2

b₁/b₂ = -1/-2 = 1/2

c₁/c₂ = -5/-p = 5/p

For parallel lines,

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

1/2 = 1/2 ≠ 5/p

So, p ≠ 5(2)

p ≠ 10

Therefore, for all real values of p except p = 10, the pair of linear equations represent parallel lines.

✦ Try This: Find the value(s) of p the pair of equations 3x - 3y -15 = 0 and 6x - 21y - p = 0, if the lines represented by these equations are parallel

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

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

3x - y - 5 = 0 and 6x - 2y - p = 0, if the lines represented by these equations are parallel. Find the value(s) of p the pair of equations

Summary:

For all the real values of p except p = 10, the lines represented by the pair of equations 3x - y - 5 = 0 and 6x - 2y - p = 0 are parallel

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