solving linear equations with 3 variables
1) x+y=1300
2) x+2z=1400
3) x+y+z=1600
this one should be so easy but i don't get which equation i should pick first?!
It does not matter which you pick.
However since there is one times x in each it is easy to eliminate x.
x + y = 1300
x + 2z = 1400
-------------- subtract
y - 2 z = -100
then do the first and the third for example
x + y = 1300
x + y + z = 1600
---------------------
subtract
-z = -300
or z = 300
That was just lucky that there is no y term
If there were we would use the two equations left with y and z to get rid of one or the other.
now with z = 300 go back and use the one in x and z to get x
x + 2(300) = 1400
I think you can take it from there.
You subtract? arent you supposed to add?
A much easier way to do this would be:
1) x+y=1300
2) x+2z=1400
3) x+y+z=1600
Look at 1 and 2. Since x+y=1300 and x+y+z=1600, z obviously equals 300. Now substitute that back in #2.
x+2(300)=1400, x+600=1400, x=800.
Now substitute x and z back in #3.
x+y+z=1600, 800+y+300=1600, 1100+y=1600, y=500
THanks Damon and Jen! (especially Jen ;)
Solving a system of linear equations with three variables requires a systematic approach. There are different methods to solve this type of problem, but I will explain one common method called "elimination method" to solve the given set of equations.
To solve the system of equations:
1) x + y = 1300
2) x + 2z = 1400
3) x + y + z = 1600
Step 1: Choose any two equations and eliminate one variable by subtracting or adding the equations. The goal is to obtain an equation with only two variables.
Since equation 1 and equation 3 both have x and y terms, let's choose these two equations to eliminate either x or y. Subtracting equation 1 from equation 3 gives:
3) (x + y + z) - (x + y) = 1600 - 1300
z = 300
Now we have eliminated the variable z and obtained the value of z as 300.
Step 2: Substitute the value of z into one of the original equations to solve for another variable. Let's substitute z = 300 into equation 2:
2) x + 2z = 1400
x + 2(300) = 1400
x + 600 = 1400
x = 1400 - 600
x = 800
Now we have obtained the value of x as 800.
Step 3: Substitute the values of x and z into another original equation to solve for the remaining variable. Let's use equation 1 to solve for y:
1) x + y = 1300
800 + y = 1300
y = 1300 - 800
y = 500
Now we have obtained the value of y as 500.
Therefore, the solution to the system of equations is:
x = 800, y = 500, z = 300.
By following these steps, you can solve the set of linear equations with three variables.