solve the system of equation
5x+2y+z=-25
5x-3y-z=-23
3x+y+2z=-9
Uggh... I am doing the same thing right now, and not fully understanding either, but I'll try to explain.
What I was told is to solve the first equation for x or another variable. In this case, it would be easier to do z because it doesn't have a number next to it. Basically, get all of the other junk on the other side so it is "z = blah blah blah."
Then, do the substitution method. If you don't know how to do this, write a response back and I'll explain more in depth. But basically, in the second and third equations, substitute z for whatever you got on the other side of the equal sign (should be -5x - 2y - 25).
That makes there only be x and y in the second and third equations. Then, if you know how, do elimination. If you don't know how to do this, either, I can explain more in depth if you respond back.
After that, solve one of the variables in the equation, and then find the other.
You should have an ordered triple instead of the ordered pair. Instead of the usual answer (x,y) it should be (x,y,z), or three answers, one for each variable.
Hopefully I helped!
now I'm confused even more
To solve the system of equations, we will use the method of elimination or substitution.
1. Elimination Method:
To eliminate one variable, we need to manipulate the equations such that when we add or subtract them, one variable will cancel out.
Let's manipulate the equations to eliminate the variable "z" first:
Equation 1: 5x + 2y + z = -25 [Multiply by -1]
Equation 2: 5x - 3y - z = -23 [Add]
After multiplying Equation 1 by -1, we get:
-5x - 2y - z = 25
Adding Equation 2 and the modified Equation 1, we have:
(5x - 3y - z) + (-5x - 2y - z) = -23 + 25
-5y = 2
Now, let's eliminate the variable "y":
Equation 2: 5x - 3y - z = -23 [Multiply by 2]
Equation 3: 3x + y + 2z = -9 [Multiply by 3]
After multiplying Equation 2 by 2 and Equation 3 by 3, we get:
10x - 6y - 2z = -46
9x + 3y + 6z = -27
Adding Equation 2 and Equation 3:
(10x - 6y - 2z) + (9x + 3y + 6z) = -46 + (-27)
19x + 4z = -73
Now we have two equations:
-5y = 2
19x + 4z = -73
To solve for "x" and "z", we need to substitute the value of "y" from the first equation into the second equation:
-5y = 2
y = -2/5
Substituting y = -2/5 into Equation 2:
19x + 4z = -73
19x + 4z = -73 [Multiply by 5]
-5y = 2 [Multiply by 19]
95x + 20z = -365
-95y = 38
Simplifying:
95x + 20z = -365
-95( -2/5 ) = 38
38x + 8z = -146
Now, we have two equations:
38x + 8z = -146
19x + 4z = -73
We can continue solving this system using either the substitution method or the elimination method.