Question

What is the classification of each system?

Drag the answers into the boxes to match each system.

A.{ x + 5y = -2{x + 5y = 4
B. { y = 3x + 4{ -2x + y = 4
C. {3x + y = 4{-6x - 2y = -8

1. Consistent independent
2. Consistent dependent
3. Inconsistent

Answer 1

Let's analyze each system of equations to classify them:

**A.**
\[
\begin{cases}
x + 5y = -2 \\
x + 5y = 4
\end{cases}
\]
These two equations represent parallel lines (same left side but different right sides), which means they have no point of intersection.
**Classification:** 3. Inconsistent

---

**B.**
\[
\begin{cases}
y = 3x + 4 \\
-2x + y = 4
\end{cases}
\]
First, let's rewrite the second equation in slope-intercept form:
\[
y = 2x + 4
\]
Now we have:
\[
\begin{cases}
y = 3x + 4 \\
y = 2x + 4
\end{cases}
\]
These two equations have different slopes (3 and 2), so they are not parallel and will intersect at one point.
**Classification:** 1. Consistent independent

---

**C.**
\[
\begin{cases}
3x + y = 4 \\
-6x - 2y = -8
\end{cases}
\]
Let's simplify the second equation:
\[
-6x - 2y = -8 \implies 3x + y = 4 \quad \text{(divide the entire equation by -2)}
\]
Thus, both equations are identical. When two equations are the same, they have infinitely many solutions (they represent the same line).
**Classification:** 2. Consistent dependent

---

Now we can summarize the classifications:

- A: **3. Inconsistent**
- B: **1. Consistent independent**
- C: **2. Consistent dependent**