Verify if the ordered pair (4, 3) is a solution of 5x − 6y = 2. Explain your reasoning.
Answer: Yes. 5(4) − 6(3) = 20 − 18 = 2, which equals the right-hand side.
Step-by-step solution
Idea: Substitute x = 4 (first number) and y = 3 (second number). If the left side comes out equal to 2, the pair is a solution.
- In (4, 3), x = 4 and y = 3.½ mark
- LHS = 5x − 6y = 5 × 4 − 6 × 3 = 20 − 18 = 2.1 mark
- RHS = 2. LHS = RHS, so the pair satisfies the equation: (4, 3) is a solution, and the point (4, 3) lies on the graph of 5x − 6y = 2.½ mark
Yes, (4, 3) is a solution because 5(4) − 6(3) = 2.
Check: Swapping the numbers gives (3, 4): 15 − 24 = −9 ≠ 2, which shows why the order in the pair matters.
Answer to write in the exam
LHS = 5x − 6y = 5(4) − 6(3) = 20 − 18 = 2
RHS = 2
LHS = RHS
∴ (4, 3) is a solution of 5x − 6y = 2
Common mistakes that cost marks
- Substituting x = 3, y = 4 and wrongly concluding it is not a solution.
- Writing “yes” without showing LHS = RHS. The reasoning is the substitution.
How this can come in the exam
Assertion–Reason (1 mark)
Assertion (A): (2, −1) is a solution of 3x + 4y = 2.
Reason (R): A pair is a solution when it makes both sides of the equation equal.
- Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
- Both Assertion (A) and Reason (R) are true, but R is not the correct explanation of A.
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
Show answer
(A) Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
3(2) + 4(−1) = 6 − 4 = 2 ✓, and R is the reason.
Try one yourself
Is (−2, 5) a solution of 4x + 3y = 7?
Show answer
4(−2) + 3(5) = −8 + 15 = 7 ✓. Yes.
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