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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=22) and (x-y=4).

Answer and explanation

Correct answer: (x=6)

The two equations describe two conditions on the same values of x and y. Since the coefficient of y is \\(-1\\) in both equations, subtraction is useful: the y terms cancel. This leaves an equation containing only x, which can be solved directly. This is the elimination method for a pair of linear equations.

Subtract the second equation from the first: \\(4x-y\\)-\\(x-y\\)=22-4\\). Simplifying gives \\(4x-y-x+y=18\\), so \\(3x=18\\). Dividing by 3 gives \\(x=6\\). Substitution also confirms the result: the second equation becomes \\(6-y=4\\), so \\(y=2\\), and the first gives \\(24-2=22\\). Therefore option A is correct.

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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