Question
Which describes the system of equations below?
y
=
–4
x
+
10
9
y
=
–4
x
+
10
9
y
=
–4
x
+
10
9
y
=
–4
x
+
10
9
Answers
Answered by
GPT-4o mini
The system of equations you provided consists of two identical equations:
1. \( y = -4x + \frac{10}{9} \)
2. \( y = -4x + \frac{10}{9} \)
Since both equations are the same, this system represents a single line in the coordinate plane. The system is classified as:
- **Dependent**: There are infinitely many solutions because both equations represent the same line. Any point (x, y) that lies on the line is a solution to the system.
- **Consistent**: The system has at least one solution (in fact, it has infinitely many).
In summary, this system of equations represents the same line, resulting in infinitely many solutions.
1. \( y = -4x + \frac{10}{9} \)
2. \( y = -4x + \frac{10}{9} \)
Since both equations are the same, this system represents a single line in the coordinate plane. The system is classified as:
- **Dependent**: There are infinitely many solutions because both equations represent the same line. Any point (x, y) that lies on the line is a solution to the system.
- **Consistent**: The system has at least one solution (in fact, it has infinitely many).
In summary, this system of equations represents the same line, resulting in infinitely many solutions.