On solving x + 3y = 13 and x + y = 7, what is the value of y?
Answer and explanation
Correct answer: y = 3
This is a pair of linear equations and is most conveniently solved by elimination because the coefficient of x is 1 in both equations. Subtract the second equation from the first: (x + 3y) − (x + y) = 13 − 7. The x terms cancel, leaving 2y = 6. Dividing by 2 gives y = 3, so option B is correct. Checking it in x + y = 7 gives x = 4, and then x + 3y = 4 + 9 = 13, confirming the solution. Values 2, 4 and 5 do not satisfy both equations simultaneously.
Frequently asked questions
What is the correct answer to this question?
y = 3
Why is this the correct answer?
This is a pair of linear equations and is most conveniently solved by elimination because the coefficient of x is 1 in both equations. Subtract the second equation from the first: (x + 3y) − (x + y) = 13 − 7. The x terms cancel, leaving 2y = 6. Dividing by 2 gives y = 3, so option B is correct. Checking it in x + y = 7 gives x = 4, and then x + 3y = 4 + 9 = 13, confirming the solution. Values 2, 4 and 5 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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