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A day full of math games & activities. Find one near you.

The pair of equations 5x - 15y = 8 and 3x - 9y = 24/5 has
a. one solution
b. two solutions
c. infinitely many solutions
d. no solution

Solution:

Given the pair of equations are

5x - 15y = 8

3x - 9y = 24/5

We have to find the solution.

We know that,

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

If a₁/a₂ = b₁/b₂ = c₁/c₂, then

i) the pair of linear equations is dependent and consistent

ii) the graph will be a pair of coincident lines. Each point on the lines will be a solution and so the pair of equations will have infinitely many solutions.

Here, a₁ = 5, b₁ = -15, c₁ = -8

a₂ = 3, b₂ = - 9, c₂ = -24/5

So, a₁/a₂ = 5/3

b₁/b₂ = -15/-9 = 5/3

c₁/c₂ = -8/(-24/5) = -40/-24 = 5/3

a1/a2 = b1/b2 = c1/c2=5/3

Therefore, the given pair of equations have infinitely many solutions.

✦ Try This: The pair of equations 2x - 16y = 8 and 4x - 28y = 16 has

Given the pair of equations are

2x - 14y = 8

4x - 28y = 16

We have to find the solution.

Here, a₁ = 2, b₁ = -14, c₁ = -8

a₂ = 4, b₂ = -28, c₂ = -16

So, a₁/a₂ = 2/4 = 1/2

b₁/b₂ = -14/-28 = 1/2

c₁/c₂ = 8/16 = 1/2

a1/a2 = b1/b2 = c1/c2=1/2

Therefore, the given pair of equations have infinitely many solutions

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

NCERT Exemplar Class 10 Maths Exercise 3.1 Sample Problem 1

The pair of equations 5x - 15y = 8 and 3x - 9y = 24/5 has, a. one solution, b. two solutions, c. infinitely many solutions, d. no solution

Summary:

The pair of equations 5x - 15y = 8 and 3x - 9y = 24/5 has infinitely many solutions.

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