After solving the linear equations `-6x+5y=2` and `-5x+6y=9`. The value of y will be :

Options

A. 3
B. 4
C. `-3`
D. `-4`.

Answer

To solve the linear equations \(-6x + 5y = 2\) and \(-5x + 6y = 9\) and find the value of \(y\), we can use the method of substitution or elimination. Here, we will use the elimination method.

### Step 1: Write down the equations
The given equations are:
1. \(-6x + 5y = 2\) (Equation 1)
2. \(-5x + 6y = 9\) (Equation 2)

### Step 2: Multiply the equations to align coefficients
To eliminate \(x\), we can multiply Equation 1 by 5 and Equation 2 by 6 to make the coefficients of \(x\) the same.

\[ 5 \times (-6x + 5y) = 5 \times 2 \implies -30x + 25y = 10 \quad (Equation 3) \]
\[ 6 \times (-5x + 6y) = 6 \times 9 \implies -30x + 36y = 54 \quad (Equation 4) \]

### Step 3: Subtract the equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \(x\):

\[ (-30x + 36y) - (-30x + 25y) = 54 - 10 \]
This simplifies to:
\[ 36y - 25y = 54 - 10 \]
\[ 11y = 44 \]

### Step 4: Solve for \(y\)
Now, divide both sides by 11 to find \(y\):

\[ y = \frac{44}{11} = 4 \]

### Final Answer
The value of \(y\) is \(4\).

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