To solve the system using the substitution method, we have the two equations:
- \( y = \frac{5}{2}x - \frac{3}{2} \) (Equation 1)
- \( 10x - 4y = 6 \) (Equation 2)
Since Equation 1 gives us \( y \) in terms of \( x \), we can substitute this expression for \( y \) into Equation 2.
Substituting \( y \) in Equation 2:
\[ 10x - 4\left(\frac{5}{2}x - \frac{3}{2}\right) = 6 \]
Distributing the \(-4\):
\[ 10x - (10x - 6) = 6 \]
Simplifying the left side:
\[ 10x - 10x + 6 = 6 \]
Thus, we have:
\[ 6 = 6 \]
This true statement indicates that there are infinitely many solutions. The equations represent the same line.
So the correct answer is: infinite solutions.