In mathematics, a pair of linear equations in two variables represents two straight-line equations that involve two unknown quantities, usually denoted by x and y These equations describe relationships between the two variables.
Pair of Linear Equations in Two Variables best notes class 10
🔹 Definition
A linear equation in two variables is an equation that can be written in the form:
🔹 Solution of a Pair of Linear Equations
The solution of a pair of linear equations is the set of values (x, y)that satisfies both equations simultaneously.
🔹 Graphical Representation
Each linear equation represents a straight line on a graph.
- One solution → Lines intersect at a point
- No solution → Lines are parallel
- Infinite solutions → Lines are coincident (overlap completely)
Pair of Linear Equations in Two Variables best notes class 10
🔹 Conditions for Solutions
🔹 Methods of Solving
- Graphical Method
- Draw both lines on graph paper.
- Find the intersection point.
- Substitution Method
- Solve one equation for one variable and substitute it into the other.
- Elimination Method
- Eliminate one variable by adding or subtracting the equations.
FAQs – Pair of Linear Equations in Two Variables
1. What is a pair of linear equations in two variables?
A pair of linear equations in two variables is a set of two equations, each of the form: ax + by = c
where xxx and y are variables and a,b,c care real numbers. The pair is solved to find the values of xxx and y that satisfy both equations.
2. What is the general form of a pair of linear equations?
3. How many solutions can a pair of linear equations have?
There are three possible cases:
- One solution (lines intersect at one point)
- No solution (lines are parallel)
- Infinite solutions (lines coincide)
4. How do you know if a pair of equations has no solution?
Check the ratio of coefficients:
5. What are the different methods of solving a pair of linear equations?
The main methods are:
- Graphical Method
- Substitution Method
- Elimination Method
- Cross Multiplication Method
6. What is the graphical representation of a pair of linear equations?
Each equation represents a straight line. The solution is the point of intersection of the two lines:
- Intersecting lines → one solution
- Parallel lines → no solution
- Coincident lines → infinite solutions
7. What is a consistent and inconsistent system?
- Consistent system: Has at least one solution (one or infinitely many)
- Inconsistent system: Has no solution
8. Can the solution be a fraction or decimal?
Yes. Solutions to linear equations can be integers, fractions, or decimal values depending on the equations.
9. Where is this topic used in real life?
- Solving age problems
- Budgeting and finance
- Business and profit analysis
- Speed–distance–time problems
- Geometry and algebra applications
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