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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 3x + 2y = 28 and mx - 2y = 12 have solution x = 5, what is the value of m?

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Answer and explanation

Correct answer: 5

A stated solution must satisfy each equation simultaneously. Insert x = 5 into the first equation: 3(5) + 2y = 28, so 15 + 2y = 28 and 2y = 13. Hence y = 13/2. Substitute x = 5 and y = 13/2 into the second equation: 5m - 2(13/2) = 12, so 5m - 13 = 12. Therefore 5m = 25 and m = 5. Option C is correct. The distractors 3, 4, and 6 would produce second-equation values of 2, 7, and 17 respectively after the known y is used, not 12.

Related tags

Pair-Linear-EquationsUnknown-ParameterKnown-SolutionAlgebraic 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?

5

Why is this the correct answer?

A stated solution must satisfy each equation simultaneously. Insert x = 5 into the first equation: 3(5) + 2y = 28, so 15 + 2y = 28 and 2y = 13. Hence y = 13/2. Substitute x = 5 and y = 13/2 into the second equation: 5m - 2(13/2) = 12, so 5m - 13 = 12. Therefore 5m = 25 and m = 5. Option C is correct. The distractors 3, 4, and 6 would produce second-equation values of 2, 7, and 17 respectively after the known y is used, not 12.

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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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. 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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