Final answer:
To solve the system of equations, we need to eliminate one variable by adding or subtracting the two equations. In this case, we will eliminate y. The solution is x = -3 and y = -2.
Step-by-step explanation:
To solve the system of equations using the elimination method, you need to eliminate one variable by adding or subtracting the two equations. In this case, we will eliminate y.
First, we will multiply the second equation by 9 to make the coefficients of y in both equations equal:
-15x + 9y = 27
-45x - 9y = 153
Adding the two equations:
-60x = 180
Dividing both sides by -60:
x = -3
Substituting the value of x into one of the original equations:
-5x - y = 17
-5(-3) - y = 17
15 - y = 17
-y = 2
Dividing both sides by -1:
y = -2
Therefore, the solution to the system of equations is x = -3 and y = -2. Option B is the correct answer.