I must solve the equation using elimination. I have have only 1 Variable on the left side of the equal sign.

( Elimination is most convenient when the variables are lined up )

2x-4y=14
4y-x=-3

You can write:

4 y - x = - 3

like:

- x + 4 y = - 3

Now:

- x + 4 y = - 3

+

2 x - 4 y = 14
_________________

- x + 2 x + 4 y - 4 y = - 3 + 14

x + 0 = 11

x = 11

4 y - x = - 3

4 y - 11 = - 3 Add 11 to both sides

4 y - 11 + 11 = - 3 + 11

4 y = 8 Divide both sides by 4

4 y / 4 = 8 / 4

y = 2

The solutions are :

x = 11 , y = 2

To solve the given system of equations using elimination, you want to eliminate one variable by adding or subtracting the equations. In this case, we can eliminate the "y" variable by lining up the equations so that the "x" terms have the same coefficient.

Given equations:
1) 2x - 4y = 14
2) 4y - x = -3

To line up the equations, we can multiply equation 2) by 2 to make the "x" coefficient the same:

1) 2x - 4y = 14
2) 8y - 2x = -6

Now, add equations 1) and 2) together:

(2x - 4y) + (8y - 2x) = 14 + (-6)

This simplifies to:

2x - 4y + 8y - 2x = 8

Now, combine like terms:

-4y + 8y = 8

4y = 8

Divide both sides by 4:

y = 2

Now that we have the value of "y", we can substitute it back into one of the original equations to solve for "x". Let's use equation 1):

2x - 4(2) = 14

Simplify:

2x - 8 = 14

Add 8 to both sides:

2x = 22

Divide both sides by 2:

x = 11

So the solution to the system of equations is x = 11 and y = 2.