Question

In linear equation $\frac{x}{3} + \frac{y}{2} = 6$ if $x = 9$ then the value of $y$ will be :

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

Multiplying the entire equation by the LCM of denominators (6) removes fractions: $2x + 3y = 36$.

Answer 1

The Correct Option is C

To solve the given linear equation \(\frac{x}{3} + \frac{y}{2} = 6\) for \(y\) when \(x = 9\), let's plug in the value of \(x\) and find \(y\).

1. Substitute \(x = 9\) in the equation: 
   \[ \frac{9}{3} + \frac{y}{2} = 6 \]
2. Simplify \(\frac{9}{3}\): 
   \[ 3 + \frac{y}{2} = 6 \]
3. Subtract 3 from both sides to isolate the \(\frac{y}{2}\) term: 
   \[ \frac{y}{2} = 6 - 3 \] \[ \frac{y}{2} = 3 \]
4. Multiply both sides by 2 to solve for \(y\): 
   \[ y = 3 \times 2 \] \[ y = 6 \]

Thus, the value of \(y\) is 6. Therefore, the correct answer is : 6.