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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Medium
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The total price of one pen and one pencil is (18) rupees. The price of (2) pens and (3) pencils is (45) rupees. What is the price of one pen?

Answer and explanation

Correct answer: 9 rupees

Let the price of one pen be ₹\(x\) and that of one pencil be ₹\(y\). Then \(x+y=18\) and \(2x+3y=45\). Multiplying the first equation by 2 gives \(2x+2y=36\). Subtracting this from the second equation gives \(y=9\). Hence, \(x=18-9=9\), so one pen costs 9 rupees. If the pen cost 10 rupees, the pencil would cost 8 rupees, which does not satisfy the second condition. Exam tip: In price-based word problems, assign separate variables to the prices and form equations first.

Related tags

Pair Of Linear EquationsElimination MethodWord ProblemsPrice ProblemsClass 10 MathematicsAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two Varia
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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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