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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Medium
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What is the value of y from 6x + 9y = 117 and 8x - 3y = 37?

Answer and explanation

Correct answer: 119/15

This is a pair of simultaneous linear equations, and elimination is efficient because multiplying the second equation by 3 creates opposite y-coefficients. From 8x - 3y = 37, obtain 24x - 9y = 111. Add this to 6x + 9y = 117: the y-terms cancel, so 30x = 228 and x = 38/5. Substitute into the second equation: 8(38/5) - 3y = 37. Since 37 = 185/5, this gives 304/5 - 3y = 185/5, so -3y = -119/5 and y = 119/15. Hence option C is correct. Checking the first equation gives 228/5 + 357/5 = 585/5 = 117. The other fractions fail this simultaneous check.

Related tags

Pair-Of-Linear-EquationsEliminationFraction-CalculationAlgebraic-MethodsMathematicsAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two Variables
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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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