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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Easy
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Find the value of (x) from (4x+y=21) and (2x+y=11).

Answer and explanation

Correct answer: (x=5)

The two equations are \\(4x+y=21\\) and \\(2x+y=11\\). Both contain the same term \\(y\\) with the same coefficient. Subtracting the second equation from the first removes \\(y\\): \\(4x+y-(2x+y)=21-11\\). This gives \\(2x=10\\), and dividing both sides by 2 gives \\(x=5\\). Therefore, option D is correct.

A quick check confirms the result. Substituting \\(x=5\\) into the second equation gives \\(2(5)+y=11\\), so \\(y=1\\). The first equation then gives \\(4(5)+1=21\\), which is also true. The key method is elimination: equal terms with equal coefficients cancel when one equation is subtracted from the other.

Related tags

Linear EquationsEliminationValue Of XEasyClass 10
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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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