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Text Solution:

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

Step 1: List the given equations.

1) 5x = y

2) z = 2y

3) x + 9 = z

Step 2: Combine any two equations.

We can combine equation 1 and equation 2. Since 5x = y, we can substitute 5x for y in equation 2, and we have the following:

$\begin{array}{l}\Rightarrow z=2y\\ \Rightarrow z=2\left(5x\right)\\ \Rightarrow z=10x\end{array}$

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

We can combine the new equation above with equation 3. Since z = 10x, we can substitute 10x for z in equation 3, and we have the following:

$\begin{array}{l}\Rightarrow x+9=z\\ \Rightarrow x+9=10x\end{array}$

Now, since we have one equation with just one variable (x), we can determine the value of that variable (x).

$\begin{array}{l}\Rightarrow x+9=10x\\ \Rightarrow 9=9x\\ \Rightarrow 1=x\end{array}$

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

We can substitute 1 for x in equation 1 in order to determine y:

$\begin{array}{l}\Rightarrow 5x=y\\ \Rightarrow 5\left(1\right)=y\\ \Rightarrow 5=y\end{array}$

LEARNING JOURNAL

What went wrong, and what can you do differently next time?

Was there a particular sticking point, breakdown in your logic or conceptual knowledge, bad habit, or careless mistake that led you to the wrong answer? At what point in your process did that error occur?

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