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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Medium
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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.

Related tags

Pair-Of-Linear-EquationsEliminationAlgebraic-ExpressionFraction-CalculationMathematicsAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two Variable
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10 more MCQs
  1. 1In the equation \(2x-y=4\), what is the value of \(y\) when \(x=3\)?
  2. 2Which equation is obtained by simplifying (6x+3y=12)?
  3. 3What is the point of intersection of the lines \(4x+3y=34\) and \(4x-y=10\)?
  4. 4If the lines \(x+y=9\) and \(kx+3y=23\) both pass through the point \(\left(4,5\right)\), what is the value of \(k\)?
  5. 5While solving a pair of linear equations in two variables by the elimination method, in which situation can one variable be eliminated directly?
  6. 6What is the \(x\)-coordinate of the point of intersection of the lines \(4x+5y=31\) and \(3x-2y=1\)?
  7. 7If the two lines have a unique point of intersection (r, s) that satisfies 3r + s = 19 and r − s = 1, what is the value of r + s?
  8. 8The unique point of intersection of two lines is (r, s). If the lines are represented by 4r + s = 29 and r − s = 1, what is the value of r + s?
  9. 9What is the solution of the equations (x+y=5) and (x-y=1)?
  10. 10In the equations (2x+y=7) and (x=2), what is the value of (y)?
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