Example 1 · level 1
Solve: x + 2y = 19 and x − y = 4. What is x?
Show solution
- (1) × 1 − (2) × 1: 3y = 15 → y = 5.
- Substitute in (1): x + 10 = 19 → x = 9.
- Check (2): 1 × 9 + (−1) × 5 = 4. ✓
Answer: 9
CLASS 10 MATHS · PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Pair of linear equations in two variables
Use substitution or elimination: make one variable’s coefficients equal, subtract to remove it, solve, then back-substitute.
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Worked examples
Example 2 · level 2
Solve: 4x + 6y = 8 and 2x − 4y = 18. What is y?
Show solution
- (1) × 2 − (2) × 4: 28y = −56 → y = −2.
- Substitute in (1): 4x − 12 = 8 → x = 5.
- Check (2): 2 × 5 + (−4) × (−2) = 18. ✓
Answer: -2
Example 3 · level 3
Isha buys 1 pen and 2 notebooks for ₹142. Meera buys 1 pen and 3 notebooks for ₹198 at the same shop. What is the price of one notebook (in ₹)?
Show solution
- 1x + 2y = 142
- 1x + 3y = 198
- Subtract: −1y = −56 → y = 56. (Pen: ₹30.)
Answer: ₹56