Answer:
The given system of equations is:
-x+6y=7
6x-30y=-34
This system of equations can be represented in matrix form as:
| -1 6 | | x | | 7 |
| 6 -30 | | y | = |-34|
To determine if the system has no solutions, infinitely many solutions, or exactly one solution, we can use the method of elimination or substitution.
In this case, we can see that the second equation can be obtained by multiplying the first equation by -5, so the two equations are equivalent, meaning they represent the same line in a 2D space.
Therefore, this system of equations has infinitely many solutions.
The reasoning behind this is that when two equations represent the same line, it means that any point on that line is a solution to the system of equations. Since a line goes on indefinitely, it means that there are infinitely many solutions possible.
Step-by-step explanation:
