- A(−1, 2)
- B(3, 2)
- C(2, −1)
- D(0, −7)
Step-by-Step Solution
From . Then → → and . Check: ✓ and ✓. (3, 2) and (0, −7) satisfy only the first equation; (−1, 2) is the correct pair with its coordinates written the wrong way round.
Answer: C) (2, −1)
Which ordered pair satisfies BOTH and ?
Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
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**: ; .
- Multiply first by 3, second by 4: .
- Add: → . Substituting back gives .
Elimination is faster than substitution when both equations have non-trivial coefficients.
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**: ; .
- Multiply first by 3, second by 4: .
- Add: → . Substituting back gives .
Elimination is faster than substitution when both equations have non-trivial coefficients.
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For the pair 5x − 4y = 8 and 10x − 8y = 20, the two lines are:A pair of linear equations is INCONSISTENT. Which condition must its coefficients satisfy?For which values of k does the pair kx + 2y = 5 and 3x + y = 1 have a UNIQUE solution?The pair 2x + 3y = 7 and (k − 1)x + (k + 2)y = 3k has infinitely many solutions. Find k.Solve 2/x + 3/y = 13 and 5/x − 4/y = −2 by putting 1/x = p and 1/y = q. Find x.