Ch 3 covers solving systems of two linear equations in two variables using multiple methods: graphical, substitution, elimination, and cross-multiplication. Students also learn to determine consistency of the system.
For a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0: if a₁/a₂ ≠ b₁/b₂, lines intersect (unique solution). If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, lines are parallel (no solution). If a₁/a₂ = b₁/b₂ = c₁/c₂, lines coincide (infinitely many solutions).
Substitution: solve one equation for a variable, substitute into the other. Elimination: multiply equations to equalise one variable's coefficient, then add/subtract. Cross-multiplication: x/(b₁c₂−b₂c₁) = y/(c₁a₂−c₂a₁) = 1/(a₁b₂−a₂b₁).
Download: https://ncert.nic.in/textbook/pdf/jemh103.pdf | Complete book: https://ncert.nic.in/textbook/pdf/jemh1ps.zip
When the lines are parallel — they have the same slope but different y-intercepts. Algebraically: a₁/a₂ = b₁/b₂ ≠ c₁/c₂. This system is called inconsistent.
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