Use elimination to solve the system of equations. 2x+y=4 and -4x-2y=8

No solution

Step-by-step explanation:

To use elimination method, we need to choose a variable to eliminate. Let's eliminate x. To eliminate x, the x coefficient in both equations must be the same, regardless of the sign. To do so, let's multiply the first equation by 2.

(2x+y=4)2

-4x-2y=8

4x+2y=8

-4x-2y=8

Let's add both equations together.

0=8

Now that we got this far, we can see that something is wrong. This normally doesn't happen. If you notice, the second equation is the first equation but multiplied by 2. Instead, let's rewrite each equation.

2x+y=4              [subtract both sides by 2x]

y=-2x+4

-4x-2y=8           [add both sides by 4x]

-2y=4x+8          [divide both sides by -2]

y=-2x-4

If you analyze both equations, you will see that they are parallel lines. We know this because the slopes are the same, but different y-intercept. from our knowledge of parallel lines, they NEVER touch or cross. This means there would be no solution at all.