how do you work out a substitution method and elimination method?

1.  Since you already have y = -x-4 given to you, you can place that back in the first equation, like so:
4x-3(-2x-4) = 2
Distribute:
4x+6x+12 = 2
Combine like terms:
10x=-10
Divide both sides by 7:
x=-1

2.  This method is easy.  Try to find out which one would cancel out and give you one variable
To get this, multiply the first equation by 3 and the second by 2:
6x + 9y = 36
6x - 4y = 10

Now, subtract them to get rid of x:
13y = 46
y=46/13

Now, plug it back into one of the equations to solve for x (I will use the second).  Change 5 to 65/13 to make it easier to add:
3x - 2(46/13) = 5
3x - (92/13) = 65/13
3x = 157/13 (which you can turn into 12.077 to make it easier)
x = 4.026

So now you have both x and y values.

Hope this helps.  Good luck!!

Substitution:

You would plug the second equation into the first equation. *Plug y=-x-4 into the 4x-3y=2
4x-3(-x-4)=2   Distributive property
4x+3x+12=2   Common Factors
7x=-10
x=-10/7     Then plug x into equation to find y.

Elimination:
First try to find what variable would be easiest to get rid of. I would multiply the top equation by 3 and the bottom by 2, (to get rid of the y)

2 (2x+3y=12)
3 (3x-2y=5)

4x+6y=24
9x-6y=15       the 6y cancels out because you have a negative and a positive, then you add the remaining columns

13x= 39
x=3

Substitution requires us to solve for either variable, then substitute that value into the other equation. This will leave us with only one unsolved value, which we can calculate.

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

"y = -2x - 4" is already solved for y, so we'll substitute this into "4x - 3y = 2". Anywhere we see y in this equation, we'll replace it with "-2x - 4".

4x - 3(-2x - 4) = 2

Now if we expand this out, and solve for x, we get:

4x - (3 * -2x) - (3 * -4) = 2
4x - (-6x) - (-12) = 2
4x + 6x + 12 = 2
10x + 12 = 2
10x + 12 - 12 = 2 - 12
10x = -10
10x/10 = -10/10
x = -1

Now we can substitute our value for x back into both equations to determine what y equals. If our value for x is correct, y will be the same in both equations:

4(-1) - 3y = 2
-4 - 3y = 2
-4 - 3y + 4 = 2 + 4
-3y = 2 + 4
-3y = 6
-3y/(-3) = (6)/(-3)
y = (6)/(-3)
y = -2

and

y = -2(-1) - 4
y = 2 - 4
y = -2

So x = -1, y = -2


The elimination method requires us to uses addition/subtraction between multiples of the two equations to eliminate a variable. Once we have one variable, we can solve for its value:

2x + 3y = 12
3x - 2y =5

If we multiply the entire first equation by 2 and the second equation by 3, we get:

2(2x) + 2(3y) =2(12)
3(3x) - 3(2y) = 3(5)

This simplifies to:

4x + 6y = 24
9x - 6y = 15

We now add these terms, just like we'd nomally add:

4x + 6y = 24
9x - 6y = 15
----------------------
13x + 0 = 39

now we can solve for x:

13x = 39
13x/13 = 39/13
x = 3

substituting back into both equations we get:

2(3) + 3y = 12
6 + 3y = 12
6 + 3y - 6 = 12 - 6
3y = 6
3y/3 = 6/3
y = 2

and

3(3) - 2y = 5
9 - 2y = 5
9 - 2y - 9 = 5 - 9
-2y = -4
-2y/(-2) =-4/(-2)
y=2

so x = 3, y =2

Subsititution:
4x-3y=2
y=-2x-4

Next: plug in x-4. Replace the y on the first equation sooo:
4x-3(-2x-4)=2

So just do your math.
4x+6x+12=2

Do like-terms. Subtract 12 from both sides.
10x=-10

Divide 10 both sides.
x= -10/10 just simplify your problem. 1

x= -1

Now for elimination. This is the easiest way and I prefer to use this way. Be careful with your math though.

2x+3y=12
3x-2y=5

So multiply first equation by 2. Second multiply by 3.

2(2x+3y=12)
3(3x-2y=5)

Multiply it :]

4x+6y=24
9x-6y=15

Since 6y-6y= 0. Add 4x and 9x. Add 24 and 15.
So:
13x=39
x=3.

Substitution:

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

The problem gives you what y is already, so substitute it to the first equation:

4x - 3 (-x - 4) = 2_______Plug in -x - 4 for y because y = -x - 4

4x + 3x +12 = 2________Distribute 3 to (-x - 4)

7x + 12 = 2____________Add: 4x + 3x

7x = -10_______________Subtract 12 from both sides

x = -10 / 7_____________Here's x

y = -(-10 / 7) - 4_________Plug in -10 / 7 for x

y = (10 / 7) - 4__________Subtract

y = -18 / 7_____________Here's y.

----------
Elimination:

2x + 3y =12
3x - 2y = 5_____________The equation is positive so add like-terms

But first, multiply them to get the like-terms the same.

Let's try:

(2x + 3y =12)____multiply by 2
(3x - 2y = 5)_____multiply by 3

4x + 6y =24
9x -  6y =15______Now add.

13x + 0y = 39

13x = 39_________Divide by 13

x = 3____________Here's x

you could do the same for y, but lets substitute 3 for x:

Use ANY equation.

2 (3) + 3y =12______sub in the 3 for x

6 + 3y = 12________2 (3) = 6

3y = 6_____________Subtract both sides by 6

3y / 3 = 6 / 3________divide by 3

y = 2______________Here's y.

Wow. Any questions?  Hope it really helped ya