The graphs of a pair of linear equations are seen to cross at the point (−1, 2). Which pair could it be?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations

A $x + y = 1$ and $x - y = 3$
B $2 x + y = 0$ and $3 x + y = 1$
C $x + 2 y = 3$ and $3 x + y = - 1$
D $x - 2 y = 3$ and $x + y = 1$

Step-by-Step Solution

Put

x = - 1, y = 2

into BOTH equations of each pair. For the answer:

- 1 + 2 (2) = 3

✓ and

3 (- 1) + 2 = - 1

✓. In the first two options the point satisfies only the first equation, and in the last option only the second. Checking just one equation of a pair is exactly the shortcut that makes students pick a wrong option.

Answer: C)

x + 2 y = 3

and

3 x + y = - 1

Key idea: Elimination method

**Steps**:
1. Multiply one or both equations by chosen numbers so coefficients of ONE variable become equal (in magnitude).
2. Add or subtract to ELIMINATE that variable.
3. Solve the resulting one-variable equation.
4. Plug back to find the other.

**Example**: