Question

Match the system of equations to the number of solutions it has.

(3 points)

y = 5x + 7

3y - 15x = 21

y = - 13x - 4

= 3x + 6

y = 5x - 1

y = 5x + 2

No Solution

::One Solution

:: Infinite Solutions

Answer 1

To determine the number of solutions for each system of equations, we should analyze if the equations represent parallel lines (no solutions), identical lines (infinite solutions), or intersecting lines (one solution).

1. **y = 5x + 7**
**3y - 15x = 21:**
Rewrite the second equation:
\[
3y = 15x + 21 \implies y = 5x + 7.
\]
These two equations are identical, hence they have **Infinite Solutions**.

2. **y = -13x - 4**
**y = 3x + 6:**
These lines have different slopes (-13 and 3), so they will intersect at one point. Thus, we have **One Solution**.

3. **y = 5x - 1**
**y = 5x + 2:**
Both lines have the same slope (5), but different y-intercepts (-1 vs. 2), making them parallel lines. Consequently, there are **No Solution**.

### Summary
- **(y = 5x + 7, 3y - 15x = 21)**: Infinite Solutions
- **(y = -13x - 4, y = 3x + 6)**: One Solution
- **(y = 5x - 1, y = 5x + 2)**: No Solution