Solve the system of equations with ROWOPS program. I know how to do the first step but after that it gets difficult for me, this is the system of equations:
3x + y - z = 1
x + 2y - z = 0
2x - y + z = 4
I used to be able to do these but now I'm getting a little rusty. Thanks for the help!
Get two independent equations in x and y only by
(1) adding the last two equations
(2) subracting equation 2 from equation 1
Here's what you get
(a) 3x +y = 4
(b) 2x -y = 1
Add those two to get rid of y and you will can easily solve for x. It equals 1. Take it from there.
I have no idea what ROWOPS means
ROWOPS is apparently a fancy new-math name for what I just did in my previous answer. It involve Operations on Rows (equations).
To solve the system of equations using ROWOPS (Operations on Rows), you need to perform operations on the equations to eliminate variables and obtain a simplified form of the system.
Let's start from the system of equations you provided:
1) 3x + y - z = 1
2) x + 2y - z = 0
3) 2x - y + z = 4
To simplify the system using ROWOPS, follow these steps:
Step 1: Add the last two equations (2) and (3) to eliminate the variable z:
(x + 2y - z) + (2x - y + z) = 0 + 4
x + 2y + 2x - y = 4
3x + y = 4 --> Equation (a)
Step 2: Subtract equation (2) from equation (1) to eliminate the variable z again:
(3x + y - z) - (x + 2y - z) = 1 - 0
2x - y = 1 --> Equation (b)
Now you have two simplified equations, (a) and (b), in terms of x and y only.
To find the values of x and y, you can solve these equations simultaneously:
(a) 3x + y = 4
(b) 2x - y = 1
You can now use various methods like substitution or elimination to solve this system of equations. For example, using the elimination method, you can add equations (a) and (b) to eliminate y:
(3x + y) + (2x - y) = 4 + 1
5x = 5
x = 1
Once you have the value of x, you can substitute it back into either equation (a) or (b) to find the value of y. Using equation (b):
2(1) - y = 1
2 - y = 1
y = 1
So the solution to the system of equations is x = 1 and y = 1.
To find the value of z, you can substitute x = 1 and y = 1 into any of the original equations. Let's use equation (2):
1 + 2(1) - z = 0
1 + 2 - z = 0
3 - z = 0
z = 3
Therefore, the solution to the system of equations is x = 1, y = 1, and z = 3.
Note: ROWOPS is just a term for the operations performed on the rows (equations) of the system to simplify it. It is not a specific program or tool.