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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 x from x/5 + y/6 = 7 and x - y = 6?

Answer and explanation

Correct answer: 240/11

Start with x - y = 6, which gives x = y + 6. To clear the denominators 5 and 6 in x/5 + y/6 = 7, multiply the entire equation by their least common multiple, 30. This produces 6x + 5y = 210. Substitution gives 6(y + 6) + 5y = 210, so 11y + 36 = 210 and 11y = 174. Hence y = 174/11. Now calculate x: x = y + 6 = 174/11 + 66/11 = 240/11. Therefore option C is correct. A check confirms x - y = 66/11 = 6, and substituting the values into the fractional equation gives 7. The other choices result from arithmetic or denominator-clearing errors.

Related tags

Pair-Of-Linear-EquationsFraction-EquationsSubstitutionAlgebraic-MethodsAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematics
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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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