Pair of Linear Equations in Two Variables — Chapter Summary
Telangana Board · Class 10 · Mathematics
Summary of Pair of Linear Equations in Two Variables for Telangana Board Class 10 Mathematics. Part of the Telangana Board Class 10 Mathematics syllabus.
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Overview
A pair of linear equations in two variables is a basic tool for solving situations with two unknown quantities. A linear equation in two variables has the form ax + by + c = 0, where a² + b² ≠ 0. The graph of such an equation is a straight line. When two such equations are considered together, the g
Key Concepts
A linear equation in two variables
A linear equation in two variables has the form ax + by + c = 0, where a² + b² ≠ 0. It represents a straight line on a graph.
Two linear equations in the same
Two linear equations in the same two variables form a pair of linear equations. A pair can be written as a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, wi
A pair of values of x
A pair of values of x and y that satisfies both equations together is called a solution of the pair.
One equation with two unknowns has
One equation with two unknowns has many solutions. Two independent equations are needed to get a unique solution.
The graph of each linear equation
The graph of each linear equation is a straight line. The point where the two lines meet gives the solution, if they intersect. If the lines are paral
Learning Objectives
- Understand what a linear equation in two variables means.
- Represent real-life situations using two linear equations.
- Identify the solution of a pair of linear equations as a common pair of values of x and y.
- Use graphical, substitution, and elimination methods to solve pairs of linear equations.
- Classify pairs of equations as consistent, inconsistent, or dependent.
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