Solve the system using the substitution method. For the system that does not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. Express numbers as integers or simplified fractions. \( \begin{array}{l}9 x+7 y=20 \\ 4 x+3 y=9\end{array} \) The system has one solution. The solution set is \( \{\square, \square)\} \). The system has no solution \( \} \). The system is inconsistent. The system has infinitely many solutions. The solution set is \( \{(x, y) \mid \square\} \). The system is inconsistent. The equations are dependent.

To solve the system using substitution, we first isolate one variable in one of the equations. Let's start with the second equation \(4x + 3y = 9\): 1. Solve for \(y\): \[ 3y = 9 - 4x \implies y = \frac{9 - 4x}{3} \] 2. Substitute this expression for \(y\) into the first equation \(9x + 7y = 20\): \[ 9x + 7\left(\frac{9 - 4x}{3}\right) = 20 \] \[ 9x + \frac{63 - 28x}{3} = 20 \] Multiply every term by 3 to eliminate the fraction: \[ 27x + 63 - 28x = 60 \] \[ -x + 63 = 60 \] \[ -x = -3 \implies x = 3 \] 3. Use \(x = 3\) to find \(y\): \[ y = \frac{9 - 4(3)}{3} = \frac{9 - 12}{3} = \frac{-3}{3} = -1 \] The solution set is \( \{(3, -1)\} \), and the system has one solution. The solution set is \(\{(3, -1)\}\).