Question

What is the solution to the system of equations?
2z−3y+z=−195
x+y−z=−7
−x+6y−z=35

Answer 1

To find the solution to the system of equations, we can use the method of substitution or elimination.

Let's solve it using elimination method:

1) 2z - 3y + z = -195
2) x + y - z = -7
3) -x + 6y - z = 35

First, let's eliminate x. We can do this by adding equation 2) and equation 3):

2) x + y - z = -7
+
3) -x + 6y - z = 35
--------------------
4) 7y = 28
y = 4

Now, substitute the value of y into equation 2):

2) x + y - z = -7
x + 4 - z = -7
x - z = -11 (Equation 5)

Next, substitute the value of y into equation 3):

3) -x + 6y - z = 35
-x + 6(4) - z = 35
24 - x - z = 35
-x - z = 35 - 24
-x - z = 11

Now, we have two equations:

Equation 5: x - z = -11
Equation 6: -x - z = 11

If we add these two equations, we eliminate x:

5) x - z = -11
6) -x - z = 11
----------------
7) -2z = 0
z = 0

Substitute the value of z into equation 5):

5) x - z = -11
x - 0 = -11
x = -11

Finally, substitute the values of x and z into equation 2:

2) x + y - z = -7
-11 + 4 - 0 = -7
-7 = -7

The solution to the system of equations is x = -11, y = 4, z = 0.