Find the value of x from the equations 5x − y = 9 and 2x − y = 3.
Answer and explanation
Correct answer: x = 2
The governing concept is the elimination method for a pair of linear equations. In 5x − y = 9 and 2x − y = 3, the coefficients and signs of y are identical, so subtracting the second equation from the first removes y: (5x − y) − (2x − y) = 9 − 3, giving 3x = 6. Dividing both sides by 3 gives x = 2. Therefore, option B is correct. Option A would produce 5 − y = 9 and 2 − y = 3, which cannot hold together; options C and D similarly fail when substituted into both original equations.
Frequently asked questions
What is the correct answer to this question?
x = 2
Why is this the correct answer?
The governing concept is the elimination method for a pair of linear equations. In 5x − y = 9 and 2x − y = 3, the coefficients and signs of y are identical, so subtracting the second equation from the first removes y: (5x − y) − (2x − y) = 9 − 3, giving 3x = 6. Dividing both sides by 3 gives x = 2. Therefore, option B is correct. Option A would produce 5 − y = 9 and 2 − y = 3, which cannot hold together; options C and D similarly fail when substituted into both original equations.
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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