The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 have
a. unique solution
b.exactly two solutions
c. infinitely many solutions
d. no solution

Solution:

Given, the pair of equations are

x + 2y + 5 = 0

-3x - 6y + 1 = 0

We have to find the solution.

Here, a₁ = 1, b₁ = 2, c₁ = 5

a₂ = -3, b₂ = -6, c₂ = 1

So, a₁/a₂ = 1/-3 = -(1/3)

b₁/b₂ = 2/-6 = -(1/3)

c₁/c₂ = 5/1

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

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

Therefore, the pair of equations has no solution.

✦ Try This: The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 have

Given, the pair of equations are

3x + 2y + 5 = 0

-9x - 6y + 4 = 0

We have to find the solution.

Here, a₁ = 3, b₁ = 2, c₁ = 5

a₂ = -9, b₂ = -6, c₂ = 4

So, a₁/a₂ = 3/-9 = -(1/3)

b₁/b₂ = 2/-6 = -(1/3)

c₁/c₂ = 5/4

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

Therefore, the pair of equations has no solution

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

NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 2

The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 have, a. a unique solution, b. exactly two solutions, c. infinitely many solutions, d. no solution

Summary:

The pair of equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 have no solution.

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