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Mathematics

The solution of the simultaneous equations 3x - 2y = 5 and x + 2y = -1 is :

  1. x = 1, y = 1

  2. x = 1, y = -1

  3. x = -1, y = 1

  4. x = -1, y = -1

Linear Equations

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Answer

Given,

Equations: 3x - 2y = 5, x + 2y = -1

⇒ 3x - 2y = 5

⇒ 3x - 5 = 2y

⇒ y = 3x−52\dfrac{3x - 5}{2}     ….(1)

Substituting value of y from equation (1) in x + 2y = -1, we get :

⇒ x + 2(3x−52)2\Big(\dfrac{3x - 5}{2}\Big) = -1

⇒ x + 3x - 5 = -1

⇒ 4x = -1 + 5

⇒ 4x = 4

⇒ x = 44\dfrac{4}{4}

⇒ x = 1.

Substituting value of x in equation (1), we get :

⇒y=3x−52⇒y=3×1−52⇒y=−22⇒y=−1.\Rightarrow y = \dfrac{3x - 5}{2} \\[1em] \Rightarrow y = \dfrac{3 \times 1 - 5}{2} \\[1em] \Rightarrow y = \dfrac{-2}{2} \\[1em] \Rightarrow y = -1.

Hence, option 2 is the correct option.

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