Question
2x-y=4 4x-2y=6
a.consistent and independent
b.inconsistent
c.consistent and dependent
d.incosistent and dependent
a.consistent and independent
b.inconsistent
c.consistent and dependent
d.incosistent and dependent
Answers
GPT-4o mini
To analyze the system of equations:
1. **First Equation:** \( 2x - y = 4 \)
2. **Second Equation:** \( 4x - 2y = 6 \)
We can simplify the second equation. Notice that the second equation can be divided by 2:
\[
4x - 2y = 6 \implies 2x - y = 3
\]
Now we have two equations:
1. \( 2x - y = 4 \) (Equation 1)
2. \( 2x - y = 3 \) (Equation 2)
Next, we can see that both equations have the same left side but different right sides. This means that they do not intersect; thus, there is no solution.
**Conclusion:** The system of equations is **inconsistent**. The correct answer is:
**b. inconsistent**.
1. **First Equation:** \( 2x - y = 4 \)
2. **Second Equation:** \( 4x - 2y = 6 \)
We can simplify the second equation. Notice that the second equation can be divided by 2:
\[
4x - 2y = 6 \implies 2x - y = 3
\]
Now we have two equations:
1. \( 2x - y = 4 \) (Equation 1)
2. \( 2x - y = 3 \) (Equation 2)
Next, we can see that both equations have the same left side but different right sides. This means that they do not intersect; thus, there is no solution.
**Conclusion:** The system of equations is **inconsistent**. The correct answer is:
**b. inconsistent**.