Solving the following system of equations using the elimination method. 3x - 4y = -4, x + 3y = -10
A. (-2, -4)
B. (-4, -2)
C. (-16, 2)
D. (-16, -2)
To solve this system of equations using the elimination method, we'll first multiply the second equation by -3 to make the coefficients of x in both equations the same:
3x - 4y = -4
-3(x + 3y) = -3(-10)
Which simplifies to:
3x - 4y = -4
-3x - 9y = 30
Now, add the two equations together:
(3x - 4y) + (-3x - 9y) = -4 + 30
-13y = 26
y = -2
Next, substitute the value of y into one of the original equations to solve for x. Let's use the first equation:
3x - 4(-2) = -4
3x + 8 = -4
3x = -12
x = -4
Therefore, the solution to the system of equations is (-4, -2), and the correct answer choice is B. (-4, -2).