A pair of equations consists of two mathematical statements connected by conditions like “and” or “or” to find the values of variables. These equations can be linear quadratic or other types. Solving them involves finding solutions that satisfy both equations simultaneously and understanding their relationship is key to solving problems in algebra geometry and real-life situations.
Class 10 Maths Chapter 3 focuses on Pair of Linear Equations in Two Variables for the CBSE Exam 2024-25. It covers solving equations using graphical and algebraic methods like substitution elimination and cross-multiplication. Students learn to find solutions that satisfy both equations and understand their applications in real-life situations. The chapter emphasizes the importance of consistency and inconsistency in equations and prepares students for problem-solving in exams and beyond.
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The system of equations given is:
1. 2x + 3y = 6 .(i)
2. 4x + 6y = 12 .(ii)
Multiply equation (i) by 2:
(2 × 2x) + (2 × 3y) = 2 × 6
⇒ 4x + 6y = 12 .(iii)
Equation (iii) is identical to equation (ii), i.e., both equations are the same line.
Because both equations are equal, the system possesses infinitely many solutions.
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