Find the solution of 2x + 5y = 26 and 3x + 5y = 29 by elimination.
Answer and explanation
Correct answer: (3, 4)
Use elimination because the y-coefficients are equal in the two equations. Subtract the first equation from the second: (3x + 5y) − (2x + 5y) = 29 − 26. The y terms cancel, leaving x = 3. Substitute x = 3 into the first equation: 2(3) + 5y = 26, so 6 + 5y = 26 and 5y = 20. Therefore y = 4, giving the solution (3, 4). Option D is correct. Checking it in the second equation gives 3(3) + 5(4) = 9 + 20 = 29. The other ordered pairs do not satisfy both equations simultaneously.
Frequently asked questions
What is the correct answer to this question?
(3, 4)
Why is this the correct answer?
Use elimination because the y-coefficients are equal in the two equations. Subtract the first equation from the second: (3x + 5y) − (2x + 5y) = 29 − 26. The y terms cancel, leaving x = 3. Substitute x = 3 into the first equation: 2(3) + 5y = 26, so 6 + 5y = 26 and 5y = 20. Therefore y = 4, giving the solution (3, 4). Option D is correct. Checking it in the second equation gives 3(3) + 5(4) = 9 + 20 = 29. The other ordered pairs do not satisfy both equations simultaneously.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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