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प्रश्न
Solve the following system of equations by the elimination method:
`x/2 + y/3 = 3, 3x + y = 12`
बेरीज
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उत्तर
Given system of equations:
`x/2 + y/3 = 3, 3x + y = 12`
Step 1: Eliminate fractions in the first equation by multiplying both sides by 6 (LCM of 2 and 3):
`6 xx (x/2 + y/3) = 6 xx 3`
⇒ 3x + 2y = 18
Now system becomes:
3x + 2y = 18 ...(i)
3x + y = 12 ...(ii)
Step 2: Eliminate (x) by subtracting equation (ii) from equation (i):
(3x + 2y) – (3x + y) = 18 – 12
⇒ 3x – 3x + 2y – y = 6
⇒ y = 6
Step 3: Substitute (y = 6) into equation (ii):
3x + 6 = 12
⇒ 3x = 6
⇒ x = 2
The solution to the system is x = 2, y = 6.
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