Solve the system of equations:
x - y - z = 2
x + 2y - 2z = 3
3x - 2y - 4z = 5
I know how to do the whole process, but sometimes I make careless errors that I never catch when I go over my work. This is the answer I worked out:
x = 5
y = 1
z = 2
could somebody please let me know if I'm correct?
to check if your answers are correct just plug in the values you found into each of the equations.
Make sure they work for all 3 equations, answers might work in one equation but not in the other. In that case you would have made a mistake.
BTW, you are right!
thanks reiny =)
To solve the system of equations:
Step 1: Write the system of equations in matrix form:
[1 -1 -1 | 2]
[1 2 -2 | 3]
[3 -2 -4 | 5]
Step 2: Use a matrix method, such as Gaussian elimination or matrix inversion, to solve the system.
Using Gaussian elimination, we start by getting a zero in the first position of the second row:
R2 = R2 - R1: (subtract the first row from the second row)
[1 -1 -1 | 2]
[0 3 -1 | 1]
[3 -2 -4 | 5]
Next, get a zero in the first position of the third row:
R3 = R3 - 3R1: (subtract three times the first row from the third row)
[1 -1 -1 | 2]
[0 3 -1 | 1]
[0 1 1 | -1]
Now, we can solve the rest of the system by back substitution.
From the second row, we get:
3y - z = 1 => 3y = z + 1 => y = (z + 1)/3
Substitute this expression for y into the third row:
z + 1 + z = -1 => 2z = -2 => z = -1
Substitute this value for z into the second row:
3y - (-1) = 1 => 3y + 1 = 1 => 3y = 0 => y = 0
Substitute the values for y and z into the first row:
x - 0 - (-1) = 2 => x + 1 = 2 => x = 1
So, the solution is x = 1, y = 0, and z = -1.
Based on your work, it appears that you made a mistake in the solution you obtained. The correct solution is x = 1, y = 0, and z = -1, not x = 5, y = 1, and z = 2.