Solve the following system of equations by elimination: -4x - 8y = -20 and 8x + 3y = 1

Answer 1

To solve this system of equations by elimination, we need to first multiply one or both of the equations by a constant so that when they are added together, one of the variables is eliminated.

In this case, we can multiply the first equation by 2 so that the coefficient of x in both equations is 8. The system becomes:

-8x - 16y = -40
8x + 3y = 1

Now, we add these two equations together:

(-8x - 16y) + (8x + 3y) = -40 + 1
-13y = -39
y = 3

Now that we have found the value of y, we can substitute it back into one of the original equations to solve for x. Using the second equation:

8x + 3(3) = 1
8x + 9 = 1
8x = -8
x = -1

Therefore, the solution to the system of equations is x = -1, y = 3.