If y = 2x + 3 and 5x − 2y = 1, what is the value of x?
Answer and explanation
Correct answer: 7
This is a pair of linear equations, and substitution is the most direct method because y is already expressed in terms of x. Substitute y = 2x + 3 into 5x − 2y = 1: 5x − 2(2x + 3) = 1. Distribute the minus sign to obtain 5x − 4x − 6 = 1, so x − 6 = 1 and therefore x = 7. Substituting back gives y = 2(7) + 3 = 17, and 35 − 34 = 1 confirms the result. Hence option C is correct; sign errors while expanding −2(2x+3) can lead to the distractors.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
This is a pair of linear equations, and substitution is the most direct method because y is already expressed in terms of x. Substitute y = 2x + 3 into 5x − 2y = 1: 5x − 2(2x + 3) = 1. Distribute the minus sign to obtain 5x − 4x − 6 = 1, so x − 6 = 1 and therefore x = 7. Substituting back gives y = 2(7) + 3 = 17, and 35 − 34 = 1 confirms the result. Hence option C is correct; sign errors while expanding −2(2x+3) can lead to the distractors.
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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