Solve the following system of equations by elimination. −4𝑥 − 8𝑦 = −20 8𝑥 + 3𝑦 = 1 N. (-1, 3) O. (2, 5) P. (1, 4)

Answer 1

First, we can multiply the first equation by 2 and the second equation by 4 to make the coefficients of 𝑦 the same:

-8𝑥 - 16𝑦 = -40
32𝑥 + 12𝑦 = 4

Now we can add the equations together to eliminate 𝑦:

-8𝑥 - 16𝑦 + 32𝑥 + 12𝑦 = -40 + 4
24𝑥 - 4𝑦 = -36

Now we can solve for 𝑥:

24𝑥 - 4𝑦 = -36
24𝑥 - 4(3) = -36
24𝑥 - 12 = -36
24𝑥 = -24
𝑥 = -1

Now that we have 𝑥, we can substitute it back into one of the original equations to solve for 𝑦. Let's use the first equation:

-4(-1) - 8𝑦 = -20
4 - 8𝑦 = -20
-8𝑦 = -24
𝑦 = 3

Therefore, the solution to the system of equations is 𝑥 = -1 and 𝑦 = 3, which corresponds to answer N. (-1, 3).