Question : What is the solution of the following equations?
2x + 3y = 12 and 3x – 2y = 5
Option 1: x = 3, y = 2
Option 2: x = 2, y = 3
Option 3: x = –2, y = 3
Option 4: x = 3, y = –2
Correct Answer: x = 3, y = 2
Solution :
Given: The equations are 2x + 3y = 12 and 3x – 2y = 5.
Find the values of the variables x and y by solving the simultaneous linear equations.
2x + 3y = 12 (equation 1)
3x – 2y = 5 (equation 2)
Multiply equation (1) with 2 and equation (2) with 3 and add them,
2(2x + 3y) + 3(3x – 2y) = 2 × 12 + 3 × 5
⇒ 4x + 6y + 9x – 6y = 24 + 15
⇒ 13x = 39
⇒ x = 3
Substitute the value of x in the equation (1),
2 × 3 + 3y = 12
⇒ 6 + 3y = 12
⇒ 3y = 12 – 6
⇒ 3y = 6
⇒ y = 2
Hence, the correct answer is x = 3, y = 2.
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