To solve the system of equations
- \( 3x + 7y = -17 \)
- \( -3x + 9y = -15 \)
we can use the method of substitution or elimination. Here, we'll use the elimination method.
First, let's add both equations together to eliminate \( x \):
\[ (3x + 7y) + (-3x + 9y) = -17 + (-15) \]
This simplifies to:
\[ (3x - 3x) + (7y + 9y) = -32 \]
So,
\[ 0 + 16y = -32 \]
This leads to:
\[ 16y = -32 \]
Dividing both sides by 16 gives:
\[ y = -2 \]
Now that we have \( y \), we can substitute it back into one of the original equations to solve for \( x \). We'll use the first equation:
\[ 3x + 7y = -17 \]
Substituting \( y = -2 \):
\[ 3x + 7(-2) = -17 \]
This simplifies to:
\[ 3x - 14 = -17 \]
Adding 14 to both sides gives:
\[ 3x = -3 \]
Dividing by 3:
\[ x = -1 \]
Thus, the solution to the system of equations is:
\[ x = -1, \quad y = -2 \]
In ordered pairs, the solution can be written as:
\[ (-1, -2) \]