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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Easy
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What is the value of x from 5x + y = 29 and 2x + y = 14?

Answer and explanation

Correct answer: x = 5

The governing concept is elimination by subtracting equations with equal coefficients. Both equations contain the same y-term, namely +y. Subtract the second equation from the first: (5x + y) − (2x + y) = 29 − 14. The y-terms cancel, leaving 3x = 15. Dividing by 3 gives x = 5, so option B is correct. If desired, substitute x = 5 into 2x + y = 14: 10 + y = 14, so y = 4; the first equation then gives 25 + 4 = 29, confirming the result. The values 4, 6 and 7 would produce different differences between the left sides and cannot satisfy both equations simultaneously.

Related tags

Linear EquationsElimination MethodValue Of XClass 10Algebraic 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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