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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.MediumLevel 57
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If x/3 + y/4 = 7 and x/4 + y/3 = 8, what is the value of x + y?

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Answer and explanation

Correct answer: 180/7

This is a pair of linear equations with fractional coefficients, so clearing the denominators is an efficient elimination step. Multiplying both equations by 12 gives 4x + 3y = 84 and 3x + 4y = 96. Adding these equations eliminates neither variable individually, but it directly produces 7x + 7y = 180. Dividing by 7 gives x + y = 180/7. Therefore, option B is correct. The nearby integer choices 24, 26, and 28 are not equal to 180/7; they could result from rounding or from an arithmetic error while adding the two equations.

Related tags

Pair-Linear-EquationsElimination-MethodFractional-EquationsAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

180/7

Why is this the correct answer?

This is a pair of linear equations with fractional coefficients, so clearing the denominators is an efficient elimination step. Multiplying both equations by 12 gives 4x + 3y = 84 and 3x + 4y = 96. Adding these equations eliminates neither variable individually, but it directly produces 7x + 7y = 180. Dividing by 7 gives x + y = 180/7. Therefore, option B is correct. The nearby integer choices 24, 26, and 28 are not equal to 180/7; they could result from rounding or from an arithmetic error while adding the two 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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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. 8If the unique point of intersection of two lines is (r,s) and 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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