A system of equations is a set of two or more equations with the same variables. The solution satisfies all equations simultaneously. Methods to solve include substitution elimination and graphing. Solutions can be unique infinite or no solution depending on the equations. It is widely used in real-life problem-solving.
Class 10 Maths Chapter 3 focuses on Pair of Linear Equations in Two Variables for CBSE Exam 2024-25. It covers concepts like graphical representation algebraic methods and applications. Students learn to solve equations using substitution elimination and cross-multiplication. The chapter emphasizes consistency of equations and real-life problem-solving ensuring a strong foundation in linear algebra.
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The following system of equations is given:
1. 5x + 2y = 10 .(i)
2. 10x + 4y = 20 .(ii)
Multiply equation (i) by 2:
(2 × 5x) + (2 × 2y) = 2 × 10
⇒ 10x + 4y = 20 .(iii)
Equation (iii) is identical to equation (ii), i.e., both equations represent the same line.
Because both equations are equal, the system has an infinite number of solutions.
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