If 3x − y = 12 and x + y = 8, what is the value of x?
Answer and explanation
Correct answer: x = 5
The elimination method is efficient because the y terms have opposite signs. Add the equations term by term: (3x − y) + (x + y) = 12 + 8. The terms −y and +y cancel, leaving 4x = 20. Dividing by 4 gives x = 5, so option C is correct. Substitution confirms the result: if x = 5, the first equation gives 15 − y = 12, hence y = 3; the second gives 5 + 3 = 8. Values 3, 4 and 6 would lead to inconsistent values of y in the two original equations and therefore cannot be solutions.
Frequently asked questions
What is the correct answer to this question?
x = 5
Why is this the correct answer?
The elimination method is efficient because the y terms have opposite signs. Add the equations term by term: (3x − y) + (x + y) = 12 + 8. The terms −y and +y cancel, leaving 4x = 20. Dividing by 4 gives x = 5, so option C is correct. Substitution confirms the result: if x = 5, the first equation gives 15 − y = 12, hence y = 3; the second gives 5 + 3 = 8. Values 3, 4 and 6 would lead to inconsistent values of y in the two original equations and therefore cannot be solutions.
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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