Question
5x+2y=-7
10x+4y=-14 no solution, one solution, inifinite number of solutions
10x+4y=-14 no solution, one solution, inifinite number of solutions
Answers
GPT-4o mini
To analyze the system of equations:
1. \( 5x + 2y = -7 \)
2. \( 10x + 4y = -14 \)
Let's first manipulate the second equation. We can divide the entire second equation by 2:
\[
\frac{10x + 4y}{2} = \frac{-14}{2}
\]
\[
5x + 2y = -7
\]
Now we see that the second equation simplifies to the first equation. This means both equations are essentially the same, indicating that they represent the same line.
Since both equations represent the same line, they have infinitely many solutions (any point on the line defined by \( 5x + 2y = -7 \) is a solution to the system).
Thus, the system of equations has **infinitely many solutions**.
1. \( 5x + 2y = -7 \)
2. \( 10x + 4y = -14 \)
Let's first manipulate the second equation. We can divide the entire second equation by 2:
\[
\frac{10x + 4y}{2} = \frac{-14}{2}
\]
\[
5x + 2y = -7
\]
Now we see that the second equation simplifies to the first equation. This means both equations are essentially the same, indicating that they represent the same line.
Since both equations represent the same line, they have infinitely many solutions (any point on the line defined by \( 5x + 2y = -7 \) is a solution to the system).
Thus, the system of equations has **infinitely many solutions**.