If 4x − y = 13 and x − y = 1, what is the value of x?
Answer and explanation
Correct answer: x = 4
Both equations contain the same term −y, so subtraction eliminates y without any preliminary multiplication. Subtract the second equation from the first: (4x − y) − (x − y) = 13 − 1. On simplifying, 4x − y − x + y = 12, so 3x = 12. Dividing by 3 gives x = 4, which is option C. To verify, x = 4 in x − y = 1 gives y = 3; then 4x − y = 16 − 3 = 13. The alternatives 2, 3 and 5 do not produce the same y in both equations, so they cannot be the common solution.
Frequently asked questions
What is the correct answer to this question?
x = 4
Why is this the correct answer?
Both equations contain the same term −y, so subtraction eliminates y without any preliminary multiplication. Subtract the second equation from the first: (4x − y) − (x − y) = 13 − 1. On simplifying, 4x − y − x + y = 12, so 3x = 12. Dividing by 3 gives x = 4, which is option C. To verify, x = 4 in x − y = 1 gives y = 3; then 4x − y = 16 − 3 = 13. The alternatives 2, 3 and 5 do not produce the same y in both equations, so they cannot be the common solution.
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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