If 7x - 3y = 20 and 14x + 3y = 64, what is the value of 2x + y?
Answer and explanation
Correct answer: 32/3
The governing concept is elimination in a simultaneous pair of linear equations. The y-coefficients are -3 and +3, so adding the equations removes y: (7x - 3y) + (14x + 3y) = 20 + 64. This gives 21x = 84 and therefore x = 4. Substitute x=4 in the first equation: 7(4) - 3y = 20, so 28 - 3y = 20 and 3y = 8. Hence y=8/3. The requested expression is not y alone; calculate it carefully: 2x+y = 2(4)+8/3 = 8+8/3 = 24/3+8/3 = 32/3. Thus option D is correct. The integer distractors arise from ignoring the fractional value of y or evaluating the wrong expression.
Frequently asked questions
What is the correct answer to this question?
32/3
Why is this the correct answer?
The governing concept is elimination in a simultaneous pair of linear equations. The y-coefficients are -3 and +3, so adding the equations removes y: (7x - 3y) + (14x + 3y) = 20 + 64. This gives 21x = 84 and therefore x = 4. Substitute x=4 in the first equation: 7(4) - 3y = 20, so 28 - 3y = 20 and 3y = 8. Hence y=8/3. The requested expression is not y alone; calculate it carefully: 2x+y = 2(4)+8/3 = 8+8/3 = 24/3+8/3 = 32/3. Thus option D is correct. The integer distractors arise from ignoring the fractional value of y or evaluating the wrong expression.
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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