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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Hard
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If (4x+y=22) and (3x-2y=1), what will be the value of (y)?

Answer and explanation

Correct answer: y=62/11

Solve the first equation for y: y=22-4x. Substitute this into the second equation: 3x-2(22-4x)=1. Expanding gives 3x-44+8x=1, so 11x=45 and x=45/11. Now calculate y=22-4(45/11)=242/11-180/11=62/11. Hence the correct value is y=62/11, option A. A direct check confirms that 4(45/11)+62/11=242/11=22 and 3(45/11)-2(62/11)=135/11-124/11=1. The earlier option C, y=6, is not valid: the first equation would then give x=4, but the second equation would become 12-12=0 rather than 1. The fractional result is completely acceptable because the coefficients and constants do not force integer solutions.

Related tags

Linear EquationsSubstitutionFractional SolutionClass 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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