Let's solve the system of equations step by step:

You provided the following system of equations:

1. \( y = 5x - 1 \)
2. \( y = -5x + 5 \)

### Step 1: Set the equations equal to each other
Since both equations equal \( y \), we can set them equal to each other to solve for \( x \):

\[
5x - 1 = -5x + 5
\]

### Step 2: Solve for \( x \)
Add \( 5x \) to both sides to eliminate the \( -5x \) on the right side:

\[
10x - 1 = 5
\]

Add 1 to both sides:

\[
10x = 6
\]

Divide by 10:

\[
x = \frac{6}{10} = \frac{3}{5}
\]

### Step 3: Solve for \( y \)
Now that we have \( x = \frac{3}{5} \), substitute this value back into either original equation to solve for \( y \). Let's use the first equation:

\[
y = 5\left(\frac{3}{5}\right) - 1
\]

Simplify:

\[
y = 3 - 1 = 2
\]

### Final Solution:
The solution to the system of equations is:

\[
x = \frac{3}{5}, \quad y = 2
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you solve a system of equations using the elimination method?
2. What does it mean if two lines have the same slope but different y-intercepts?
3. How do you graph the solution to this system of equations?
4. What happens if two lines in a system of equations are parallel?
5. Can you find the intersection of two non-linear equations?

**Tip:** When dealing with fractions in your solutions, it's often helpful to double-check by substituting back into the original equations to avoid any arithmetic mistakes.

Learn how to solve the system of equations 5x - 1 = -5x + 5 step-by-step with detailed explanations. This problem involves solving linear equations using the substitution method, suitable for high school students (Grades 9-12).

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