Final answer:
To solve the system of equations by elimination, you combine the equations to cancel one variable, find the value of the remaining variable, then substitute back to find the other. In this problem, the solution is x = -1 and y = -2.
Step-by-step explanation:
To solve the system of equations by elimination, we will combine the two equations to eliminate one of the variables. The system given is:
1) 5x - 9y = 13
2) -5x + 7y = -9
Add the two equations together to eliminate x:
(5x - 9y) + (-5x + 7y) = 13 - 9
-2y = 4
Now divide both sides by -2 to solve for y:
y = -2
Substitute y = -2 into one of the original equations to find x. Let's use the first equation:
5x - 9(-2) = 13
5x + 18 = 13
5x = -5
Now divide both sides by 5:
x = -1
Therefore, the solution to the system of equations is x = -1 and y = -2.