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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Hard
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What is the solution of (\frac{x}{2}+\frac{y}{5}=6) and (x-y=4)?

Answer and explanation

Correct answer: (x=\frac{68}{7},\ y=\frac{40}{7})

The direct answer is option D: x=68/7 and y=40/7. First clear the denominators in x/2+y/5=6 by multiplying every term by 10. This gives 5x+2y=60. From x-y=4, write x=y+4. Substitute: 5(y+4)+2y=60, so 7y+20=60, 7y=40, and y=40/7. Therefore x=y+4=40/7+28/7=68/7. Option D is correct. Option A has x=60/7,y=32/7; their difference is 4, but the first equation becomes 44/7, not 6. Option B has difference 4 but fails the first equation. Option C also has difference 4 but fails it. Direct checking of D gives x-y=4 and x/2+y/5=34/7+8/7=6. The memory cue is to multiply by the least common denominator before eliminating fractions.

Related tags

Linear EquationsFraction EquationsSubstitutionHardClass 10
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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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