If y = 2x − 1 and x + y = 8, what is the value of y?
Answer and explanation
Correct answer: y = 5
This question uses substitution to solve two simultaneous linear equations. Replace y in x + y = 8 by the given expression 2x − 1. Then x + (2x − 1) = 8, so 3x − 1 = 8. Adding 1 gives 3x = 9, and division by 3 gives x = 3. Using y = 2x − 1, we obtain y = 2(3) − 1 = 5. Therefore option C is correct. A quick check gives x + y = 3 + 5 = 8 and y = 6 − 1 = 5. The other proposed values do not satisfy the two equations together.
Frequently asked questions
What is the correct answer to this question?
y = 5
Why is this the correct answer?
This question uses substitution to solve two simultaneous linear equations. Replace y in x + y = 8 by the given expression 2x − 1. Then x + (2x − 1) = 8, so 3x − 1 = 8. Adding 1 gives 3x = 9, and division by 3 gives x = 3. Using y = 2x − 1, we obtain y = 2(3) − 1 = 5. Therefore option C is correct. A quick check gives x + y = 3 + 5 = 8 and y = 6 − 1 = 5. The other proposed values do not satisfy the two equations together.
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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