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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Expert
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Three pencils and two erasers cost (31) rupees. Two pencils and five erasers cost (47) rupees. What is the price of one pencil?

Answer and explanation

Correct answer: (61/11) rupees

Let the price of one pencil be \(p\) rupees and that of one eraser be \(e\) rupees. The equations are \(3p+2e=31\) and \(2p+5e=47\). Multiplying the first equation by 5 and the second by 2 gives \(15p+10e=155\) and \(4p+10e=94\). Subtracting, \(11p=61\), so \(p=\frac{61}{11}\) rupees. Therefore, option B is correct. The value 6 rupees in option C is close, but it does not satisfy the equations exactly. Exam tip: In the elimination method, make the coefficients of one variable equal before adding or subtracting the equations.

Related tags

Linear EquationsSubstitution MethodElimination MethodWord ProblemsAlgebraic 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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