Question

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

Answer 1

To solve the system of equations, we can use the method of elimination.

First, let's add the three equations together:
2z - 3y + z + x + y - z + (-x + 6y - z) = -195 - 7 + 35

Simplifying both sides gives:
3y + 7y = -195 - 7 + 35

Combining like terms gives:
10y = -167

Dividing both sides by 10 gives:
y = -16.7

Now, let's substitute the value of y back into one of the original equations. Using the second equation, we have:
x + (-16.7) - z = -7

Simplifying gives:
x - z = 8.7

Lastly, let's substitute y = -16.7 and x = 8.7 - z into the third equation:
-(8.7 - z) + 6(-16.7) - z = 35

Simplifying gives:
-8.7 + z - 100.2 - z = 35

Combining like terms gives:
-108.9 = 35

As this is not a true statement, there is no solution to the system of equations.