In each of the following questions, two equations are given. You have to solve them and give answer(निम्नलिखित प्रत्येक प्रश्न में दो समीकरण दिए गए हैं। आपको उन्हें हल करना है और उत्तर देना है
I. `7x +10y =34`
II. `11x + 13y =48` .

Options

A. `xgty`
B. `xgey`
C. `x lty`
D. x = y or relationship can not be established( x = y या संबंध स्थापित नहीं किया जा सकता)

Answer

To solve the given equations step by step, we will use the elimination method.

### Step 1: Write the equations
We have the two equations:
1. \( 7x + 10y = 34 \) (Equation 1)
2. \( 11x + 13y = 48 \) (Equation 2)

### Step 2: Eliminate one variable
To eliminate \( y \), we will make the coefficients of \( y \) in both equations equal. The coefficient of \( y \) in Equation 1 is 10 and in Equation 2 is 13.

We can multiply Equation 1 by 13 and Equation 2 by 10:

- From Equation 1:
\[ 13(7x + 10y) = 13(34) \implies 91x + 130y = 442 \quad (Equation 3) \]

- From Equation 2:
\[ 10(11x + 13y) = 10(48) \implies 110x + 130y = 480 \quad (Equation 4) \]

### Step 3: Subtract the equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \( y \):
\[ (110x + 130y) - (91x + 130y) = 480 - 442 \]
This simplifies to:
\[ 110x - 91x = 480 - 442 \]
\[ 19x = 38 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{38}{19} = 2 \]

### Step 5: Substitute \( x \) back to find \( y \)
Now that we have \( x = 2 \), we can substitute this value back into one of the original equations to find \( y \). We will use Equation 1:
\[ 7(2) + 10y = 34 \]
\[ 14 + 10y = 34 \]
\[ 10y = 34 - 14 \]
\[ 10y = 20 \]
\[ y = \frac{20}{10} = 2 \]

### Step 6: Conclusion
We find that \( x = 2 \) and \( y = 2 \). Therefore, \( x \) is equal to \( y \).

### Final Answer
The relationship between \( x \) and \( y \) is that \( x = y \).

### Options:
- a) \( x > y \)
- b) \( x \geq y \)
- c) \( x < y \)
- d) \( x = y \) or relationship cannot be established

The correct option is **d) \( x = y \)**.

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