Solve the system by the addition method.
\[
\begin{array}{c}
x+3 y=9 \\
3 x+2 y=-1
\end{array}
\]
Answer
The solution to the system of equations is \(\boxed{x = -3}\) and \(\boxed{y = 4}\). This means that these values satisfy both equations simultaneously.
Step 1 ：We are given the system of equations: \[\begin{array}{c} x+3 y=9 \\ 3 x+2 y=-1 \end{array}\]
Step 2 ：We can solve this system by the addition method, also known as the method of elimination. This method involves adding or subtracting the equations in order to eliminate one of the variables.
Step 3 ：First, we multiply the first equation by 3 and the second equation by 1. This gives us the new system of equations: \[\begin{array}{c} 3x+9 y=27 \\ 3 x+2 y=-1 \end{array}\]
Step 4 ：Next, we subtract the second equation from the first to eliminate y. This gives us the equation: \[x = -3\]
Step 5 ：Once we have the value of x, we can substitute it back into the first equation to find the value of y. Substituting x = -3 into the first equation gives us: \[ -3 + 3y = 9 \] which simplifies to \[y = 4\]
Step 6 ：The solution to the system of equations is \(\boxed{x = -3}\) and \(\boxed{y = 4}\). This means that these values satisfy both equations simultaneously.
