Answer:
There are infinitely many solutions.
Step-by-step explanation:
So there are three possible scenarios. The is a finite set of solutions, there are infinitely many solutions, or there are no solutions.
We can determine which of these scenarios is possible by analyzing the pair of equations.
Y = (1/4)x - 1
Y = (1/4)(x - 4)
For clarity, I have put parentheses around the fractional component 1/4.
Note, the first equation can be rewritten as such:
Y = (1/4)x - 1
Y = (x/4) - 1
And the second equation can be simplified using the distributive property of multiplication
Y = (1/4)(x - 4)
Y = (1/4)x - (1/4)(4)
Y = (x/4) - (1)
Y = (x/4) - 1
Notice, both equation are actually the same. This means whatever values of x or Y you put in, the two equations will always be equal. This means there are infinitely many solutions because there are an infinite combination of x and Y that solve pair of equations given, which is actually the same equation. In the graph, this is represented as a line on top of the existing line.
Cheers.
