Chapter 3 · Class 10 CBSE · Formula Sheet
Pair of Linear Equations in Two Variables Formulas — Class 10 CBSE
Solve pairs of linear equations graphically and algebraically using substitution and elimination.
Key Formulas
Consistent (Unique Solution)
\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}
Consistent (Infinite Solutions)
\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}
Inconsistent (No Solution)
\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}
Substitution Method
\text{Express one variable in terms of other, substitute}
Elimination Method
\text{Make coefficients equal, add/subtract equations}
Cross-Multiplication
\dfrac{x}{b_1c_2 - b_2c_1} = \dfrac{y}{c_1a_2 - c_2a_1} = \dfrac{1}{a_1b_2 - a_2b_1}
Worked Examples
1Using: Supplementary Angles
If one angle is 65 degrees, find its supplement.
Step 1: Supplement = 180 - 65
Step 2: = 115 degrees.
Answer: 115 degrees
2Using: Vertically Opposite
Two lines intersect. If one angle is 40 degrees, find the vertically opposite angle.
Step 1: Vertically opposite angles are equal.
Step 2: The angle = 40 degrees.
Answer: 40 degrees
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