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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.MediumLevel 57
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If 2x−7y=5 and 4x+7y=43, which pair of x and y is correct?

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Answer and explanation

Correct answer: x=8, y=11/7

Add the two equations because the y-coefficients are −7 and +7. We obtain (2x−7y) + (4x+7y) = 5 + 43, so 6x = 48 and x = 8. Substitute x = 8 into the first equation: 2(8) − 7y = 5, which gives 16 − 7y = 5, so 7y = 11 and y = 11/7. Therefore the correct ordered pair is (8, 11/7), option A. Verification in the second equation gives 4(8) + 7(11/7) = 32 + 11 = 43. Options B, C and D fail either the first equation, the second equation, or both, so they are not solutions of the simultaneous system.

Related tags

Pair-Of-Linear-EquationsElimination-MethodOrdered-PairAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

x=8, y=11/7

Why is this the correct answer?

Add the two equations because the y-coefficients are −7 and +7. We obtain (2x−7y) + (4x+7y) = 5 + 43, so 6x = 48 and x = 8. Substitute x = 8 into the first equation: 2(8) − 7y = 5, which gives 16 − 7y = 5, so 7y = 11 and y = 11/7. Therefore the correct ordered pair is (8, 11/7), option A. Verification in the second equation gives 4(8) + 7(11/7) = 32 + 11 = 43. Options B, C and D fail either the first equation, the second equation, or both, so they are not solutions of the simultaneous system.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..

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  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. 8If the unique point of intersection of two lines is (r,s) and 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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