Let's transform the given system of equations with fractions into a system with integer coefficients.
Here are the equations provided:
[tex]\[ \frac{2}{3}x + \frac{3}{5}y = \frac{172}{15} \][/tex]
[tex]\[ \frac{7}{8}x + 3y = 77 \][/tex]
### Step-by-Step Solution:
1. Clear the Fractions in the First Equation:
[tex]\[ \frac{2}{3}x + \frac{3}{5}y = \frac{172}{15} \][/tex]
Find the least common multiple (LCM) of the denominators 3, 5, and 15, which is 15.
Multiply both sides of the equation by 15:
[tex]\[ 15 \left(\frac{2}{3}x\right) + 15 \left(\frac{3}{5}y\right) = 15 \left(\frac{172}{15}\right) \][/tex]
Simplify:
[tex]\[ 5 \cdot 2x + 3 \cdot 3y = 172 \][/tex]
[tex]\[ 10x + 9y = 172 \][/tex]
2. Clear the Fractions in the Second Equation:
[tex]\[ \frac{7}{8}x + 3y = 77 \][/tex]
Multiply both sides of the equation by 8 to eliminate the fraction:
[tex]\[ 8 \left(\frac{7}{8}x\right) + 8 \cdot 3y = 8 \cdot 77 \][/tex]
Simplify:
[tex]\[ 7x + 24y = 616 \][/tex]
The resulting system of equations with integer coefficients is:
[tex]\[ 10x + 9y = 172 \][/tex]
[tex]\[ 7x + 24y = 616 \][/tex]
### Conclusion:
Therefore, the correct answer is:
[tex]\[ \text{d.} \ 10x + 9y = 172 \][/tex]
[tex]\[ \phantom{\text{d.} \ } 7x + 24y = 616 \][/tex]
