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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 6x - 5y = 8 and 9x + 10y = 83, what is the value of x + y?

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Answer and explanation

Correct answer: 307/35

To eliminate y, multiply 6x - 5y = 8 by 2, obtaining 12x - 10y = 16. Add this to 9x + 10y = 83. The y terms cancel and give 21x = 99, so x = 33/7. Substitute this into the first equation: 6(33/7) - 5y = 8, hence 198/7 - 5y = 56/7 and 5y = 142/7. Thus y = 142/35. Therefore x + y = 33/7 + 142/35 = 165/35 + 142/35 = 307/35. Option B is correct. The integer options 8, 9, and 10 are only rough numerical neighbours and are not the exact value.

Related tags

Pair-Linear-EquationsElimination-MethodLinear-ExpressionAlgebraic 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?

307/35

Why is this the correct answer?

To eliminate y, multiply 6x - 5y = 8 by 2, obtaining 12x - 10y = 16. Add this to 9x + 10y = 83. The y terms cancel and give 21x = 99, so x = 33/7. Substitute this into the first equation: 6(33/7) - 5y = 8, hence 198/7 - 5y = 56/7 and 5y = 142/7. Thus y = 142/35. Therefore x + y = 33/7 + 142/35 = 165/35 + 142/35 = 307/35. Option B is correct. The integer options 8, 9, and 10 are only rough numerical neighbours and are not the exact value.

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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