Question

−4x − 8y = −20
8x + 3y = 1
show every step

Answer 1

To solve this system of equations using the elimination method, we can multiply the first equation by 2 and the second equation by 4 to make the coefficients of either x or y in both equations equal. This will allow us to eliminate one variable when adding or subtracting the two equations.

1) -8x - 16y = -40 (Multiply the first equation by 2)
2) 32x + 12y = 4 (Multiply the second equation by 4)

Now, let's add the two equations together to eliminate x:
-8x - 16y + 32x + 12y = -40 + 4
24x - 4y = -36

Divide all terms by 4:
6x - y = -9

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

-4x - 8y = -20
-4x - 8(-9) = -20
-4x + 72 = -20
-4x = -92
x = 23

Now, we can substitute x = 23 back into the second original equation to solve for y:

8(23) + 3y = 1
184 + 3y = 1
3y = -183
y = -61

Therefore, the solution to the system of equations is x = 23 and y = -61.