Answer: B: (7, -4)
Explanation:
To solve for x and y, we can use either substitution or elimination method. Here, we'll use the elimination method to solve for x and y:
2x - 4y = 36 (Equation 1)
4x + 3y = -5 (Equation 2)
To eliminate y, we can multiply Equation 1 by 3 and Equation 2 by 2, and then add the two resulting equations:
6(2x - 4y) = 6(36) (Multiplying Equation 1 by 3)
2(4x + 3y) = 2(-5) (Multiplying Equation 2 by 2)
Simplifying, we get:
12x - 24y = 216
8x + 6y = -10
Adding the two equations, we get:
20x = 206
Dividing both sides by 20, we get:
x = 10.3
Now, substituting x = 10.3 into Equation 1 or Equation 2, we can solve for y. Let's use Equation 1:
2x - 4y = 36
2(10.3) - 4y = 36
20.6 - 4y = 36
-4y = 15.4
y = -3.85
Therefore, the solution to the system of equations is (x,y) = (10.3,-3.85).
Rounded to the nearest integer, the solution is approximately (x,y) = (10,-4).
So, the answer is option B: (7, -4).