I want to know about no solution Related: Graphical - Linear Equations Part 2?

Question

I want to know about no solution Related:  Graphical - Linear Equations Part 2?

Answer

No solution is that solution in which a1/a2 is equal to b1/b2 but b1/b2 is not equal to c1/c2

Answer

Its to simple

when
a1/a2=b1/b2 is not equal to c1/c2
in this case,

the pair of linear equation has no solution.

for ex-
6x-3y+10=0
2x-y+9=0

here,
3/1(6/2)=3/1(-3/-1)is not equal to 10/9

Answer

No Solution in Graphical Representation of Linear Equations
In the context of linear equations, the term 'no solution' refers to a situation where two lines representing the equations do not intersect at any point. This means there are no values for the variables that satisfy both equations simultaneously.
Understanding Linear Equations
- A linear equation can be represented in the form:
y = mx + b
where:
- m = slope of the line
- b = y-intercept
- When visualized graphically, each linear equation corresponds to a straight line on the Cartesian plane.
Conditions for No Solution
- Parallel Lines:
- When the slopes (m) of the two lines are equal but the y-intercepts (b) are different, the lines are parallel.
- Example:
- Equation 1: y = 2x + 3
- Equation 2: y = 2x - 1
- These lines will never meet, indicating no solution.
- Graphical Representation:
- In a graphical representation, the absence of an intersection point signifies that there are no common solutions.
Implications of No Solution
- In practical scenarios, this often indicates conflicting constraints or requirements in a given problem, making it impossible to satisfy all conditions simultaneously.
- Understanding this concept is essential in fields like economics, engineering, and physics, where relationships between variables are modeled through linear equations.
By recognizing the characteristics of linear equations and their graphical representation, one can effectively identify scenarios where no solutions exist.

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