Simultaneous Equation - 2x+3y=8,2x-3y=2?

Question

To solve to get X by Elimination you would get 2.5 however I can not get this value by Subsitution. Where am I going wrong?

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

y=(2x+8)/3

2x-3(2x+8)/3 = 2

2x-3(2x+8) = 6

2x-6x+24=6

-4x=-18

x=4.5

Answer 1

2x+3y=8
2x-3y=2
3y=8-2x
y=(8-2x)/3
2x-3(8-2x)/3=2
multiplying by 3
6x-24+6x=6
12x=30
x=2.5
substituting y=(8-5)/3
=1
so x=2.5 and y=1

Answer 2

You can use elimination by simply adding up the 2 equations"

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

Adding both equations we have:

4x = 10 => x = 2.5

and hence y = (2x-2) / 3 = 1

Both these values satisfy the given equation.

In your calculations, you are substituting y = (2x + 8) / 3 using the first equation, which is an incorrect procedure. The actual value of y using the first equation is:

2x +3y = 8 => 3y = 8 - 2x => y = (8 - 2x ) / 3

Hence y must be substituted as (8 - 2x ) / 3 and not as you mentioned. You made a simple, silly error.

Answer 3

Add the two simultaneous equations. This eliminates the terms in ''y'.
So we have 4x = 10
x = 2.5

By your method y = (8 - 2x) / 3 NB you have omitted to change the sign from + to - in front of the 2x as it moves across the 'equals' sign. Hence
2x - 3(8-2x)/3 = 2
2x - (8-2x) = 2
2x - 8 + 2x = 2 NB In removing the brackets the two minuses , before '2x' become a '+'.
Collecting terms
4x - 8 = 2 Removing the '-8' across the 'equals' it changes sign to '+'.
4x = 8 + 2
4x = 10
x = 2.5
When 'x' = 2.5 and substitute in
We have
2(2.5) + 3y = 8
5 +3y = 8
3y = 8 - 5
3y = 3
y =1
I hope this helps.

Answer 4

Add the 2 equations together and you get 4x=10 as the y terms have been eliminated. Therefore X=10/4 which is 2.5.

x=2.5

Substitute this into one of the equations e.g. 2x-3y=2 and you get 5-3y=2 therefore 2+3y=5 meaning y=1.

x=2.5 and y=1.

Substitute these into the other equation 2x+3y=8 and that confirms that x=2.5 and y=1.

Answer 5

As everyone has said, you've gone wrong right at the beginning. If you take it in stages, you get :- 3y=8-2x
Or :- y=(8-2x)/3. However, a number of people have pointed out that this is not the best way to solve this particular equation. In this case it is easier to simply add the two equations together. So we get :- 2x+3y+2x-3y=10 which leaves us with :- 4x=10 so x=2.5

Putting this value in either of the original equations will yield a value of :- y=1.

Answer 6

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

add together

4x = 10
x = 2.5

substitute in second line

2x - 3y = 2

x = 2.5

Therefore

5 + 3y = 8
3y = 8 - 5
3 y = 3
y = 1

substitute in line 2

2x - 3y = 2

5 - 3 = 2

Answer 7

2x+3y=8 (1)
2x-3y=2 (2) Adding:

4x =10
x =10/4
x =2.5

From (1) 2(2.5) + 3y = 8
5 + 3y = 8
3y =8-5
3y = 3
y = 3/3
y = 1

so {x=2.5, y=1}

Check using (2)....2(2.5) - 3(1) = 2 Correct!

Answer 8

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

these two equations are
equivalent to a single equation
saying 0=10 or 0= -10 which is a
nonsense

assume that the equations are:-
2x+3y=8.....(1)
2x-3y=2......(2)
from (1),x=(8-3y)/2
substitute into (2)
2(8-3y)/2-3y=2
8-3y-3y=2
>>> -6y=-6
>>>>>y=1
substitute back into (1)
2x+3=8
>>>>x=5/2

therefore,x=5/2,y=1

i hope that this helps

Answer 9

We have 2x+3y=8
& 2x -3y=2
Adding these gives 4x=10 Therefore x=10/4=2.5

Answer 10

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

I selected the second equation to solve for x.

2x=3y+2
x=3/2y+1

Apply that (x value) equation to the first equation to get a value for y.

2(3/2y+1)+3y=8
3y+2+3y=8
6y+2=8
6y=6
y=1

Now, insert that value into the second equation to get a numeric value of x.

2x-3(1)=2
2x-3=2
2x=5
x=5/2

Check:

2(5/2)+3(1)=8
5+3=8
8=8 yes

2(5/2)-3(1)=2
5-3=2
2=2 yes