https://r2.erweima.ai/mathbot/image/172601038839610it21fi.jpg

The system of linear equations presented in the image is:

\[
\begin{cases}
2x + y = 1 \\
x - y = 5
\end{cases}
\]

We can solve this system using either substitution or elimination. Let's use substitution for this case:

### Step 1: Solve one equation for one variable
From the second equation:

\[
x - y = 5 \quad \Rightarrow \quad x = y + 5
\]

### Step 2: Substitute this into the first equation
Now, substitute \(x = y + 5\) into the first equation:

\[
2(y + 5) + y = 1
\]

### Step 3: Simplify and solve for \(y\)

\[
2y + 10 + y = 1
\]
\[
3y + 10 = 1
\]
\[
3y = 1 - 10
\]
\[
3y = -9
\]
\[
y = -3
\]

### Step 4: Substitute \(y = -3\) back into the expression for \(x\)

Substitute \(y = -3\) into \(x = y + 5\):

\[
x = -3 + 5 = 2
\]

### Final Answer:
The solution to the system of equations is:
\[
x = 2, \quad y = -3
\]

Would you like more details or have any questions?

Here are five related questions to expand the topic:

1. How would you solve this system using the elimination method?
2. What happens if both equations represent the same line?
3. How can you check if the solution is correct?
4. How does this method change if the system has no solution (parallel lines)?
5. How would you graphically represent this system of equations?

**Tip:** Substitution is a great method to use when one of the equations is already solved or easily solvable for one variable.

Solve the system of linear equations: 2x + y = 1, x - y = 5.

Learn how to solve the system of linear equations 2x + y = 1 and x - y = 5 using the substitution method. This step-by-step solution is suitable for students in Grades 8-10 and covers key algebraic concepts.

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