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For the following two (02) items: Let (2x + 3y) = 1 2 and (3x + 2y) = 3 2 , where - How many values does (x + y) have?

Options

  1. ATwo
  2. BThree
  3. CFour
  4. DMore than four

Correct answer

C. Four

Step-by-step solution

Let 2x + 3y = u and 3x + 2y = v . Given u = 1 2 and - Given v = 3 2 and - Adding the two equations, we get u + v = 5(x + y) x + y = u + v 5 . The possible values of u + v are: 3 + 6 = 2 3 - 6 = 6 - 3 + 6 = - 6 - 3 - 6 = - 2 Since all four values of u + v are distinct, there are exactly four distinct values for x + y .

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