Write a pair of linear equations which has the unique solution x = - 1, y = 3. How many such pairs can you write
Solution:
Condition for the pair of systems to have a unique solution is a₁/a₂ ≠ b₁/b₂
Let us consider the linear equations in two variables,
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
We have x = - 1 and y = 3 as the unique solution of these two equations.
Hence, it must satisfy the above equations
a₁(-1) + b₁(3) + c₁ = 0
- a₁ + 3b₁ + c₁ = 0 ------------------------ (1)
a₂(- 1) + b₂(3) + c₂ = 0
- a₂ + 3b₂ + c₂ = 0 ----------------------- (2)
Different values of a₁, b₁, c₁ and a₂, b₂, c₂ satisfy the Equations (1) and (2).
Therefore, infinitely many pairs of linear equations are possible.
✦ Try This: Write a pair of linear equations which has the unique solution x = - 2, y = 5. How many such pairs can you write
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 6
Write a pair of linear equations which has the unique solution x = - 1, y = 3. How many such pairs can you write
Summary:
A pair of linear equations x = - 1, y = 3 has infinitely many pairs of linear equations.
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