32. Solve $x^{2}+y=7$ for $x$ and $y$. \[ 3 x+y=9 \]

Step 1 ：We have a system of two equations with two variables, $x$ and $y$. The equations are $x^{2}+y=7$ and $3x+y=9$.

Step 2 ：We can solve this system by substitution or elimination. Let's use substitution. First, we solve the second equation for $y$, which gives us $y = 9 - 3x$.

Step 3 ：We then substitute $y$ into the first equation, which gives us $x^{2} + 9 - 3x = 7$.

Step 4 ：Solving this equation gives us two possible values for $x$, which are $x = 1$ and $x = 2$.

Step 5 ：Substituting these values of $x$ back into the equation $y = 9 - 3x$ gives us corresponding values of $y$, which are $y = 6$ and $y = 3$.

Step 6 ：Thus, the solutions to the system of equations are \(\boxed{(x, y) = (1, 6)}\) and \(\boxed{(x, y) = (2, 3)}\).