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General
Easy

Question

x + 2y = 16
0.5x - y = 10
The solution to the system of equations above is (x, y). What is the value of x ?

  1. -2
  2. 2
  3. 18
  4. 36

The correct answer is: 18


    HINT: Solve the system of equations.
    Complete step by step solution:
    Let x + 2y = 16…(i) and 0.5x - y = 10…(ii)
    Multiply (ii) with 2 to make the coefficients of y to be the same.
    On multiplying, we get (ii) to be 2(0.5x - y = 10) = x - 2y = 20
    Let x - 2y = 20…(iii)
    On adding (i) and (iii),
    Then, LHS becomes 2x and RHS will be 16 + 20 = 36
    On equating LHS and RHS, we get 2x = 36
    On dividing both the sides by 2, we get fraction numerator 2 straight x over denominator 2 end fraction space equals space 36 over 2
    x = 18
    Thus the value of x is 18
    Hence option C is the correct answer.
    Note: We can solve this by multiplying (i) with 0.5. We get (i) to be 0.5x + y = 8 and let this be (iii).By solving (ii)
    and (iii), we get the value of y = -1 .By substituting the value of y in (ii) we get the value of x to be 18.

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