classify each system and determine the number of solutions: 5x-y=-3 and 15x-3y=-9
infinite solutions. they are the same line.
To classify the system and determine the number of solutions, we need to determine if the system is consistent or inconsistent, and if it is consistent, determine if it is dependent or independent.
Let's start by rearranging the equations in standard form, which is in the form ax + by = c.
Given system of equations:
1) 5x - y = -3
2) 15x - 3y = -9
To convert equation 1 into standard form, let's add y to both sides:
5x = y - 3
Now, let's rearrange equation 2 into standard form by dividing both sides by 3:
5x - y = -3
By comparing the two equations, we can see that they are identical, which means they represent the same line.
Since the two equations represent the same line, they are dependent. This means that they have infinitely many solutions. Any point on the line described by these equations will satisfy both equations simultaneously.
In summary, the given system of equations is dependent and has infinitely many solutions.