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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.Easy
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If y = x − 3 and 2x + y = 15, what is the value of x?

Answer and explanation

Correct answer: x = 6

The governing concept is the substitution method. One equation already expresses y in terms of x: y = x − 3. Substitute this expression into the second equation, 2x + y = 15, to obtain 2x + (x − 3) = 15. Combining like terms gives 3x − 3 = 15. Adding 3 to both sides results in 3x = 18, and division by 3 gives x = 6. Therefore option C is correct. To verify, use x = 6 in the first relation: y = 6 − 3 = 3. The second equation then becomes 2(6) + 3 = 12 + 3 = 15, so the result is consistent. The values 4, 5, and 7 produce corresponding y-values that do not satisfy the second equation.

Related tags

Linear EquationsSubstitution MethodValue Of XClass 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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