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Text Solution:

Let’s follow the steps we learned above to determine z:

Step 1: List the given equations.

1) x + y = 11

2) z $–$ y = 4

3) 2x + 6 = z

Step 2: Combine any two equations.

We can combine equation 1 and equation 2. We can use the combination method of adding the two equations in order to cancel the variable y:

$\begin{array}{l}x+y=11\\ \underset{¯}{+z-y=4}\\ x+z+y-y=11+4\\ x+z+0=15\\ x=15-z\end{array}$

Step 3: Combine the simplified equation with the remaining untouched equation, and then solve for an unknown variable.

Next, we can combine the new equation above with equation 3. Since x = 15 $–$ z, we can substitute 15 $–$ z for x in equation 3, and we have the following:

$\begin{array}{l}\Rightarrow 2x+6=z\\ \Rightarrow 2\left(15-z\right)+6=z\\ \Rightarrow 30-2z+6=z\\ \Rightarrow 36=3z\\ \Rightarrow z=12\end{array}$

Step 4: If required, plug the value found into the equations in order to find the values of the other variables.

In this case, we are looking for the value of z, so we do not need to find x or y.