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Answer Key: Pair of Linear Equations in Two Variables PYQ

Class: 10 (CBSE) Subject: Mathematics Chapter: 03
BOARD EXAM 2025 (Set 30/6/3)
Q8. The system of equations \(y + a = 0\) and \(2x = b\) has
  • (A) No solution
  • (B) \((-a, \frac{b}{2})\) as its solution
  • (C) Infinite solutions
  • (D) \((\frac{b}{2}, -a)\) as its solution
Q25 (a). Solve the following pair of equations algebraically: \(101x + 102y = 304\), \(102x + 101y = 305\)
Adding: \(203x + 203y = 609 \Rightarrow x + y = 3\). Subtracting: \(x - y = 1\).
Solving: \(x = 2, y = 1\).
OR
Q25 (b). In a pair of supplementary angles, the greater angle exceeds the smaller by \(50�\). Express the given situation as a system of linear equations and find the measure of each angle.
Q26. Check whether the given system of equations is consistent or not. If consistent, solve graphically: \(x - 2y = 0\), \(2x + y = 0\)
\(a_1/a_2 = 1/2\), \(b_1/b_2 = -2\). Since \(a_1/a_2 \neq b_1/b_2\), lines intersect. System is consistent. Solution: \(x = 0, y = 0\).