Let us consider the equation 3x + 2y = 12. What about the ordered pair (1, 3)?
Answer: (1, 3) is not a solution: 3 × 1 + 2 × 3 = 9 ≠ 12.
Step-by-step solution
Idea: An ordered pair (x, y) is a solution only if putting x and y into the equation makes the left side equal the right side exactly.
- Put x = 1 and y = 3 in the left side: 3x + 2y = 3 × 1 + 2 × 3 = 3 + 6 = 9.½ mark
- 9 ≠ 12, so the equation is not satisfied. (1, 3) is not a solution of 3x + 2y = 12.½ mark
(1, 3) is not a solution of 3x + 2y = 12, because 3(1) + 2(3) = 9 ≠ 12.
Check: Compare with a real solution: (2, 3) gives 6 + 6 = 12 ✓, so changing x from 2 to 1 breaks the equation.
Answer to write in the exam
LHS = 3x + 2y = 3(1) + 2(3) = 9
RHS = 12
LHS ≠ RHS
∴ (1, 3) is not a solution of 3x + 2y = 12
Common mistakes that cost marks
- Substituting the other way round (x = 3, y = 1): 9 + 2 = 11. In an ordered pair the first number is always x.
- Stopping after finding one value “close” to 12. A solution must give exactly 12.
How this can come in the exam
MCQ (1 mark)
Which ordered pair is a solution of 4x + y = 10?
- (1, 5)
- (2, 2)
- (3, 1)
- (2, 3)
Show answer
(B) (2, 2)
4(2) + 2 = 10 ✓. The others give 9, 13 and 11.
Try one yourself
Is (3, −1) a solution of 2x − 5y = 11?
Show answer
2(3) − 5(−1) = 6 + 5 = 11 ✓. Yes.
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