Solve the system: x + y + z = 3, 2x – y + 3z = 3, x - 2y + 3z = 0

Sure, let's solve this system of equations step by step.

Step 1: Let's start by subtracting the third equation from the second to eliminate y:

2x - y + 3z = 3 x - 2y + 3z = 0

This gives us:

x + y = 3

Step 2: Now, let's subtract the first equation from this new equation to eliminate x:

x + y = 3 x + y + z = 3

This gives us:

z = 0

Step 3: Now that we know z = 0, we can substitute z into the first and second equations to solve for x and y:

x + y + 0 = 3 2x - y + 3*0 = 3

This simplifies to:

x + y = 3 2x - y = 3

Step 4: Adding these two equations together gives:

3x = 6

So, x = 2.

Step 5: Substituting x = 2 into the first equation gives:

2 + y = 3

So, y = 1.

Therefore, the solution to the system of equations is x = 2, y = 1, z = 0.