We are given three equations:

1. $x + y = 7$
2. $y + z = 4$
3. $x + z = 3$

To find $x + y + z$, we can add all three equations:

$(x + y) + (y + z) + (x + z) = 7 + 4 + 3$ $2x + 2y + 2z = 14$

Now, divide both sides by 2:

$x + y + z = 7$

So, $x + y + z = 7$.

Solving for $x$, $y$, and $z$:

We now know that $x + y + z = 7$. Using this, we can substitute into the original equations.

Step 1: Solve for $x$

From equation $x + z = 3$, and knowing $x + y + z = 7$, we can express $y$ as: $y = 7 - (x + z) = 7 - 3 = 4$

Step 2: Solve for $z$

Substitute $y = 4$ into the second equation $y + z = 4$: $4 + z = 4$ $z = 0$

Step 3: Solve for $x$

Substitute $z = 0$ into the third equation $x + z = 3$: $x + 0 = 3$ $x = 3$

Final values:

• $x = 3$
• $y = 4$
• $z = 0$

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. If $x - y = 2$ and $y + z = 6$, what is $x + z$?
2. Solve for $x$, $y$, and $z$ if $x + 2y = 8$, $y + z = 5$, and $z - x = 1$.
3. What is the sum of $x + y + z$ if $x = 4$, $y = -2$, and $z = 5$?
4. If $x + y = 10$, $y + z = 12$, and $z + x = 8$, find $x$, $y$, and $z$.
5. Solve the system: $2x + 3y = 13$, $x - y = 2$.

Tip: When solving systems of linear equations, adding or subtracting equations can help simplify and eliminate variables quickly.