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Both (2, −1) and (a, 3) lie on the line . Find a.

Class 9Linear Equations in Two VariablesLinear Equations
  • A−6
  • B6
  • C−3
  • D3

Step-by-Step Solution

First check (2, −1): 2 + 2(−1) = 0 ✓. Now a + 2(3) = 0 → a + 6 = 0 → a = −6. Check: −6 + 6 = 0 ✓.
Answer: A) −6

Key idea: Graphing a linear equation

Three steps:

1. Find at least **two solutions** (preferably the and intercepts — easiest to plot).
2. Plot those points on the coordinate plane.
3. Draw a straight line through them.

Every linear equation in two variables graphs as a STRAIGHT LINE. (That's why they're called 'linear'.)

For accuracy: find a third solution and verify it lies on the line — catches arithmetic mistakes.

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