# Thread: Linear Equations in 4 variables..

1. ## Linear Equations in 4 variables..

Hey guys, I'm having a lot of trouble with this problem:

5x + 4y = 29
y + z - w = -2
5x + z = 23
y - z + w = 4

Yeah, I don't even know where to start on this one, so any kind of help would be greatly appreciated.

2. Originally Posted by asdfasdf
Hey guys, I'm having a lot of trouble with this problem:

5x + 4y = 29
y + z - w = -2
5x + z = 23
y - z + w = 4

Yeah, I don't even know where to start on this one, so any kind of help would be greatly appreciated.
there are so many ways to attack a problem like this. tell us what method you must use to solve it

3. Originally Posted by Jhevon
there are so many ways to attack a problem like this. tell us what method you must use to solve it
The instructions just say to solve it algebraically.

4. Originally Posted by asdfasdf
The instructions just say to solve it algebraically.
oh. well in that case. you are to use the equations to try and eliminate some variables so you can solve for others. similar to what you would do if it were just 2 simultaneous equations (you can solve such systems right?).

for example, note that we can solve for y by adding the second and fourth equations

5. Originally Posted by Jhevon
oh. well in that case. you are to use the equations to try and eliminate some variables so you can solve for others. similar to what you would do if it were just 2 simultaneous equations (you can solve such systems right?).

for example, note that we can solve for y by adding the second and fourth equations
yes. in the past I've dealt with solving these types of equations in 2 variables. However, although that is really easy, for some reason I just can't find the relationship between solving an equation with only 2 variables to solving an equation like this one..I understand that I can solve for y in the 2nd and 4th equations, and the answer would be y = 1, but where would I go from there?

6. Originally Posted by asdfasdf
yes. in the past I've dealt with solving these types of equations in 2 variables. However, although that is really easy, for some reason I just can't find the relationship between solving an equation with only 2 variables to solving an equation like this one..I understand that I can solve for y in the 2nd and 4th equations, and the answer would be y = 1, but where would I go from there?
well, one way would be to replace y with one in all the other equations, so now you only have 3 variables to worry about.

another way would be to continue like nothing happened, and try to add/subtract other sets of equations to eliminate other variables. sometimes you won't be left with just one variable as you were with y. but you can add/subtract the new equations you form to eliminate other variables until you are left with one.

7. Originally Posted by Jhevon
well, one way would be to replace y with one in all the other equations, so now you only have 3 variables to worry about.
ok..that made things much easier because i found an example in my book of a problem with 3 variables...thanks much for your help