Evaluate x + y, if 217x + 131y = 913 and 131x + 217y = 827.

Options

A. 5
B. 4
C. 7
D. `-8`

Answer

To solve the equations \( 217x + 131y = 913 \) and \( 131x + 217y = 827 \) and find \( x + y \), follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( 217x + 131y = 913 \) (Equation 1)
2. \( 131x + 217y = 827 \) (Equation 2)

### Step 2: Add the two equations
Add Equation 1 and Equation 2:
\[ (217x + 131y) + (131x + 217y) = 913 + 827 \]
This simplifies to:
\[ (217 + 131)x + (131 + 217)y = 1740 \]
\[ 348x + 348y = 1740 \]

### Step 3: Factor out the common term
We can factor out 348 from the left side:
\[ 348(x + y) = 1740 \]

### Step 4: Solve for \( x + y \)
Now, divide both sides by 348:
\[ x + y = \frac{1740}{348} \]

### Step 5: Simplify the fraction
Now, simplify \( \frac{1740}{348} \):
\[ x + y = 5 \]

### Final Answer
Thus, the value of \( x + y \) is \( 5 \).

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