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Try solving the system of equations algebraically and describe the result that you get. 

Show your work.

To solve this system of equations, let's examine the two equations:

\[
y = \frac{4}{5}x - 3
\]
\[
y = \frac{4}{5}x + 1
\]

Since both equations are equal to \( y \), we can set the right-hand sides of each equation equal to each other:

\[
\frac{4}{5}x - 3 = \frac{4}{5}x + 1
\]

### Step 1: Eliminate \( \frac{4}{5}x \) from both sides
Subtract \( \frac{4}{5}x \) from both sides:

\[
-3 = 1
\]

This statement, \( -3 = 1 \), is a contradiction, which means there is no solution to this system of equations.

### Conclusion
The system of equations is **inconsistent**. This indicates that the lines represented by these equations are **parallel** (they have the same slope, \( \frac{4}{5} \), but different \( y \)-intercepts) and will never intersect.

Would you like further details or have any questions?

### Related Questions
1. How do you determine if two lines are parallel using their equations?
2. What are the conditions for a system of linear equations to have no solution?
3. How would the solution differ if the equations had the same \( y \)-intercept?
4. What does it mean for a system of equations to be consistent or inconsistent?
5. Can we determine the type of solution by looking at the slopes and intercepts?

### Tip
To quickly determine if two lines are parallel, check if they have the same slope but different \( y \)-intercepts. Parallel lines never intersect, so they have no common solution.

Try solving the system of equations algebraically and describe the result that you get. Show your work.

Discover how to solve the system of equations y = (4/5)x - 3 and y = (4/5)x + 1. Follow a step-by-step solution to determine if there’s an intersection or if the lines are parallel. This problem highlights key algebraic concepts suitable for students in Grades 9-10.

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