What number of solutions would this system of equations have?𝑦=𝑥−5y=x−5𝑦=𝑥+3y=x+3

1. Break Down the Problem

We need to analyze the given system of equations:

1. $y = x - 5$
2. $y = x + 3$

2. Relevant Concepts

To determine the number of solutions for this system, we will observe the graphical representation of the two equations. Each equation represents a line in the Cartesian plane. The number of solutions to this system corresponds to the number of intersection points of the two lines.

3. Analysis and Detail

To find the number of solutions, we will set the two equations equal to each other since both equal $y$: $x - 5 = x + 3$

Now, we can simplify this equation:

$x - x - 5 = 3 \\ -5 = 3$

The statement $-5 = 3$ is a contradiction, meaning that the two equations represent parallel lines that never intersect.

4. Verify and Summarize

Since we derived a contradiction, we can conclude that there are no points at which these two lines intersect. Therefore, the system of equations has no solutions.

Final Answer

The system of equations has 0 solutions.