
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

Excluding the unknown $y$ from the system of equations

$$
\begin{aligned}
& a_{1} x+b_{1} y=c_{1} \\
& a_{2} x+b_{2} y=c_{2}
\end{aligned}
$$

we obtain

$$
x=\frac{c_{1} b_{2}-c_{2} b_{1}}{a_{1} b_{2}-a_{2} b_{1}}
$$

Write the formula for $y$ without further calculations.

Present the answer in LaTex format: \boxed{Your answer}
user