Solve by addition?

Question

x - 2y = 4

2x - y = 4

Answer 1

ellimination by addition Method

x - 2y = 4- - - - -Equation 1
2x - y = 4- - - - -Equation 2
- - - - - - -
Multiply equation 2 by - 2

2x - y = 4

- 2(2x) - (- 2)(y) = - 2(4)

- 4y - (- 2y) = - 8

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

x - 2y = 4
- 4x+ 2y = - 8
- - - - - - - - - -
- 3x = - 4

- 3x / - 3 = - 4 / - 3

x = - 4 / - 3

x = 4 /3

The answer is x = 4/3

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - -
x - 2y = 4

4/3 - 2y = 4

4/3 - 2y = 4

4/3 - 2y- 4/3 = 4 - 4/3

- 2y = 12/3 - 4/3

- 2y = 8/3

- 2y/- 2 = 8/3 /- 2

y = 8/3 ÷ - 2/1

y = 8/3 x 1 / - 2

y = 8 /- 6

y = - 4/3

The answer is y = - 4/3

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

x - 2y = 4

4/3 - 2(- 4/3) = 4

4/3 - (- 8/3 )= 4

4/3 + 8/3 = 4

12/3 = 4

4 = 4
- - - - - -

Check for equation 2

2x - y = 4

2(4/3) - (- 4/3) = 4

8/3 + 4/3 = 4


12/3 = 4

4 = 4

- - - - - - - -

The solution set is { 4/3. - 4/3 }

- - - - - - - - - - - - -s-

Answer 2

First multiply -2 to the first equation to obtain
-2x + 4y = -8. Note that the solution set would not be
changed. Now we consider

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

We add two equations to obtain 3y = -4. Hence, y = -4/3.
Plug y = -4/3 into any of the equations above to obtain
x = 4/3.

Answer 3

x - 2y = 4 --------Multiply by -2
2x - y = 4 ----------Multiply by 1

-2x + 4y = - 8
2x - y = 4 ------------------- adding gives:-

3y = - 4
y = - 4/3

x + 8/3 = 4
x = 4 - 8/3
x = 12/3 - 8/3 = 4/3

Answer is x = 4/3 , y = - 4/3

Answer 4

-2x+4y=-8
2x-y=4
adding
3y=-4
y=-4/3
substituting
x+8/3=12/3
x=4/3