Maths-
General
Easy

Question

x + 2y = 10
2x – y = 5
The solution to the given system of equations is (x, y). What is the value of 3x + y ?

  1. 5  
  2. 7  
  3. 13  
  4. 15  

The correct answer is: 15


    HINT: Solve the system of equations.
    Complete step by step Solution
    Given system of equations are,
    x plus 2 y equals 10...(i)
    2 x minus y equals 5…(ii)
    Multiply (i) with 2 to make the coefficients of x to be the same in both the equations.
    On multiplying, we get 2 x plus 4 y equals 20…(iii)
    On subtracting (ii) from (iii),
    We get LHS to be 2 x plus 4 y minus 2 x plus y equals 5 y
    And RHS to be 20 minus 5 equals 15
    On equating LHS and RHS,
    we get y = 3.
    On substituting y equals 3 in (i),
    We get, x equals 4.
    So the value of 3 x plus y equals 3 left parenthesis 4 right parenthesis plus 3 equals 15
    Therefore, 3 x plus y equals 15
    Hence option D is the correct answer.
    Note: We can solve this directly by adding these 2 equations. Then LHS would be 3 x plus y and RHS would be 15. Hence we get 3 x plus y equals 15.

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