Class X Mathematics
Chapter 3: Pair of Linear Equations in Two Variables
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Syllabus Sections
Key Formulas & Equations
Click Copy to duplicateSystem Consistency condition
\frac{a_1}{a_2} \neq \frac{b_1}{b_2}
Condition for a unique solution (intersecting lines).
Infinite Solutions condition
\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}
Condition for coincident lines.
Related Formulas from Adjacent Chapters
Quadratic Roots Sum
\alpha + \beta = -\frac{b}{a}
[From Polynomials] Sum of roots of ax² + bx + c.
Quadratic Roots Product
\alpha \beta = \frac{c}{a}
[From Polynomials] Product of roots of ax² + bx + c.
The Quadratic Formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
[From Quadratic Equations] Finds the exact roots of ax² + bx + c = 0.