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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Hard
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If \(2x+3y=18\) and \(5x-4y=1\), find the value of (x-2y).

Answer and explanation

Correct answer: \(-\frac{101}{23}\)

Multiply the two equations by 4 and 3 respectively to get \(8x+12y=72\) and \(15x-12y=3\). Adding them gives \(23x=75\), so \(x=\frac{75}{23}\). Substituting in \(2x+3y=18\) gives \(y=\frac{88}{23}\). Hence, \(x-2y=\frac{75}{23}-2\left(\frac{88}{23}\right)=-\frac{101}{23}\). Although \(-4\) is a nearby integer, it is not the exact value. Exam tip: when a fractional result is obtained, retain the exact fraction unless rounding is specifically asked.

Related tags

Pair Of Linear EquationsElimination MethodSubstitution MethodExact ValueClass 10 AlgebraAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two Variab
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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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