The system of equations is solved by eliminating x through addition, yielding y = -2, and substituting back to find x = -1, giving the final solutions for the variables in the system.
To solve the system of equations 3x + 7y = -17 and -3x + 9y = -15, we can begin by adding them together to eliminate the x variable. This step results in 16y = -32. Dividing through by 16, we find that y = -2. We then substitute y = -2 into one of the original equations to solve for x. Using 3x + 7(-2) = -17, we simplify to find 3x - 14 = -17. Adding 14 to both sides gives us 3x = -3, and dividing by 3, we get x = -1.
Therefore x = -1 and y = -2.
In conclusion, when solving a system of equations, combining the equations strategically can quickly simplify the problem and help us determine the values of the variables.