Solve :
` 8x + 13y - 29 =0 `
` 12 x- 7y - 17=0 `

Answer

To solve the system of equations:

1. **Given Equations:**
\[ 8x + 13y - 29 = 0 \quad \text{(Equation 1)} \]
\[ 12x - 7y - 17 = 0 \quad \text{(Equation 2)} \]

2. **Rearranging Equation 1 for x:**
\[ 8x + 13y = 29 \]
\[ 8x = 29 - 13y \]
\[ x = \frac{29 - 13y}{8} \quad \text{(Equation 3)} \]

3. **Substituting Equation 3 into Equation 2:**
Substitute \( x \) from Equation 3 into Equation 2:
\[ 12\left(\frac{29 - 13y}{8}\right) - 7y - 17 = 0 \]

4. **Clearing the fraction:**
Multiply through by 8 to eliminate the denominator:
\[ 12(29 - 13y) - 56y - 136 = 0 \]
\[ 348 - 156y - 56y - 136 = 0 \]
\[ 348 - 136 - 212y = 0 \]
\[ 212y = 348 - 136 \]
\[ 212y = 212 \]

5. **Solving for y:**
\[ y = \frac{212}{212} = 1 \]

6. **Substituting y back into Equation 1 to find x:**
Substitute \( y = 1 \) into Equation 1:
\[ 8x + 13(1) - 29 = 0 \]
\[ 8x + 13 - 29 = 0 \]
\[ 8x - 16 = 0 \]
\[ 8x = 16 \]
\[ x = \frac{16}{8} = 2 \]

7. **Final Solution:**
The solution to the system of equations is:
\[ (x, y) = (2, 1) \]