how do you solve y= 2x-4 & 2y= -x ?

2(2x-4)-4=-x
4x-8-4=-x
3x=12
x=4
2y=-4
y=-2

Value of x:
2(2x - 4) = - x
4x - 8 = - x
5x = 8
x = 8/5

Value of y (1st equation):
= 2(8/5) - 4
= 16/5 - 20/5
= - 4/5

Answer: x = 8/5, y = - 4/5

Proof (2nd equation):
2(- 4/5) = - 8/5
- 8/5 = - 8/5

Solve by using substitution

y = 2x - 4
2y = -x

2y = -x
x = 2y/(-1)
x = (-2y) ...... (1)

y = 2x - 4

Substitute (1) for x.
y = 2(-2y) - 4
y = -4y - 4
y + 4y = -4
y = -4/5 (-0.8)

y = 2x - 4

Substitute -4/5 for y.
-4/5 = 2x - 4
2x = 4 - 4/5
2x = 20/5 - 45
x = (16/5)/2
x = (16/5)(1/2)
x = 8/5 (1.6)

∴ x = 8/5 (1.6), y = -4/5 (-0.8)

When 2 equations in two unknowns are given, you are looking for values of x and y. If these were graphed, the solution would be the point where the two lines crossed.

2y = -x -----> y = -(x/2) substitute this in the other equation.

-(x/2) = 2x - 4 -----> -x = 2(2x - 4) -----> -x = 4x - 8

-5x = -8 -----> x = 8/5

Now solve for y in the other equation.

2y = -x -----> 2y = -(8/5) -----> y = -(8/10) = -(4/5)

The solution is: (8/5,-4/5)

4x-8=-x
5x=8
x=8/5
y=16/5-4=-4/5

are they the same problem or different?