Find the value of X and Y (X और Y का मान ज्ञात कीजिए)
I. `2x+3y=14`
II. `4x+2y=16`

Options

A. `xgty`
B. `xlty`
C. x=y
D. none of these(इनमें से कोई नहीं)

Answer

To solve the equations for \(X\) and \(Y\), we have the following two equations:

1. \(2x + 3y = 14\) (Equation 1)
2. \(4x + 2y = 16\) (Equation 2)

### Step 1: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 2:

\[ 2x + y = 8 \quad \text{(Equation 3)} \]

### Step 2: Solve for \(y\) in terms of \(x\)
Now, we can express \(y\) in terms of \(x\) using Equation 3:

\[ y = 8 - 2x \quad \text{(Equation 4)} \]

### Step 3: Substitute \(y\) in Equation 1
Next, we substitute Equation 4 into Equation 1:

\[ 2x + 3(8 - 2x) = 14 \]

### Step 4: Expand and simplify
Now, we expand and simplify the equation:

\[ 2x + 24 - 6x = 14 \]

Combining like terms gives:

\[ -4x + 24 = 14 \]

### Step 5: Isolate \(x\)
Now, we isolate \(x\):

\[ -4x = 14 - 24 \]
\[ -4x = -10 \]
\[ x = \frac{-10}{-4} = \frac{5}{2} \]

### Step 6: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can substitute it back into Equation 4 to find \(y\):

\[ y = 8 - 2\left(\frac{5}{2}\right) \]
\[ y = 8 - 5 = 3 \]

### Final Solution
Thus, the values of \(X\) and \(Y\) are:

\[ x = \frac{5}{2}, \quad y = 3 \]