need math help!! (solving linear systems)

need help with solving linear systems (substitution method)

1.
s = t + 4
2t + s = 19

2.

2c - d = -2
4c + d = 20

3.

2a = 8
a + b = 2

ETC..
if you can help add me: [email protected]

 

Take the first equation, "s = t + 4" and substitute it into the second equation. To do this, change all of the "s" variables in the second equation with "t + 4". This is what it looks like before and after you substitute.

2t + s = 19

turns into

2t + t + 4 = 19

Then solve the system.

3t + 4 = 19 <-- Combine like terms

3t = 15 <-- Subtract 4 over to the right side of the equation

t = 5 <-- Divide both sides by 3.

For this example, you will need to solve for a variable. Let's solve the first equation for the variable "d".

2c - d = -2

2c = -2 + d <-- Add d over to the right

2c + 2 = d <-- Add 2 over to the left

d = 2c + 2

Now that you have that done, substitute all of the "d" variables in the second equation with "2c + 2".

4c + d = 20

4c + 2c + 2 = 20 <-- Substitute in "2c + 2" for "d"

6c + 2 = 20 <-- Combine like terms

6c = 18 <-- Subtract 2 over to the right side

c = 3 <-- Divide both sides by 6

Once again, solve for one of the variables, in this case, lets solve for "a" using the first equation.

2a = 8

a = 4 <-- Divide both sides by 2

Now that we have what "a" equals, substitute that into the second equation.

a + b = 2

4 + b = 2 <-- Substitute "a" with 4.

b = -2 <-- Subtract 4 over to the left side of the equation.



If you need further help, you can message me on msn at [email protected]. You can contact me on the Sythe Ventrilo Server (My name is R33l2r3al) or you can simply PM me here on sythe.

 

Well he explained it really well, I'm try to make it simple/my way of doing it in my head witch is similar.

1
s = t + 4
2t + s = 19


2t + t + 4 = 19
3t = 15
t = 5


2
2c - d = -2
4c + d = 20

6c = 18
c = 3


3
2a = 8
a + b = 2

a = 4
4 + b = 2
b = -2


That's how I do it in my head. If you read his detailed explanation than look at my way you'll see my shortcuts.

 

thanks for the help, it helped alot