If a pair of linear equations is represented by intersecting lines graphically, then it has

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If a pair of linear equations is represented by intersecting lines graphically, then it has

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unique solution

infinitely many solutions

no solution

None

answer is A.

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Detailed Solution

Given that pair of linear equations is represented by intersecting lines graphically.
We know that the linear equation is represented in the form

a x + b y = r

.
Every equation solution that fulfills the equation must lie on the line that represents the equation.
The pair of linear equations are said to have unique solution, if

a 1 a 2 ≠ b 1 b 2

. Suppose the equations

5 x + 7 y = 50

and

7 x + 5 y = 46

.
Substitute the values into the

a 1 a 2

and

b 1 b 2 ⋅

a 1 a 2 = 57

and

b 1 b 2 = 75

. Therefore,

a 1 a 2 ≠ b 1 b 2

, this signifies that the pair of equations has a single solution.
A set of intersecting lines represents the solution.
Question Image

So, a pair of linear equations has unique solution(s) if it is represented by intersecting lines graphically.
The correct option is (1).

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