Solve the system of equations using the addition method.
-2x + 40y = 40 4x - 5y = -5
A) (0, 0)
B) (1, 1)
C) (0, 1)
D) (1, 0)

Question

Quizplus · Accepted Answer

First, we need to manipulate one of the equations so that either the x or y variable has the same coefficient in both equations. We can do this by multiplying the second equation by 10:

2x + 40y = 40 
(10)(4x - 5y = -5)

Now, we have:

2x + 40y = 40 
40x - 50y = -50

We can eliminate the y variable by adding the two equations together:

2x + 40y + 40x - 50y = 40 - 50 
42x - 10y = -10

Simplifying:

21x - 5y = -5

Now we have two equations with the same coefficients for y, so we can eliminate y again:

(5)(2x + 40y = 40)
(-21)(21x - 5y = -5)

10x + 200y = 200 
-441x + 105y = 105

Adding these two equations:

-431x + 305y = 305

We can isolate y by dividing both sides by 305:

y = 1

Now we can substitute y = 1 into either of the original equations to solve for x:

2x + 40(1) = 40

2x = 0

x = 0

Therefore, the solution to the system of equations is (0, 1), so the best choice is C.

Solve the System of Equations Using the Addition Method