Question

Solve the system. Show your step by step work.
2x+y+z=8
x+2y-z=-5
z=2x-y

Answer 1

x = 2

y = -1

z = 5

Explanation:

Let's solve the system of equations:

2x + y + z = 8

x + 2y - z = -5

z = 2x - y

First, substitute the third equation into the first two:

2x + y + (2x - y) = 8

x + 2y - (2x - y) = -5

Simplify:

4x = 8

4y = -5

Now, solve for x and y:

x = 2

y = -1

Now, substitute these values back into the third equation to find z:

z = 2(2) - (-1)

z = 5

So, the solution to the system of equations is x = 2, y = -1, and z = 5.