Final answer:
The best method to solve the given system of equations is elimination using multiplication followed by addition. After multiplying the second equation by 2.5 and adding them together, the solution to the system is found to be (3, -1).
Step-by-step explanation:
To determine the best method to solve the system of equations, let's examine the equations given:
-5x + 3y = -18
2x + 2y = 4
To use elimination, we can multiply the second equation by 2.5 to make the coefficient of x the same in both equations:
-5x + 3y = -18
5x + 5y = 10
Now, adding the two equations together eliminates x:
8y = -8
Solving for y, we get:
y = -1
Substitute y = -1 into the second original equation:
2x + 2(-1) = 4
2x - 2 = 4
2x = 6
x = 3
The solution is the pair (3, -1). The correct answer aligns with the substitution method, but the solution presented in the question is slightly different, showing (3, -2). This suggests a typo in the options given by the student. The correct option should be (3, -1).