How many solutions does this system of equations have?

It looks like you have several topics in your question! Let’s focus on one area.

If we take “slope-intercept form” as the main topic, the slope-intercept form of an equation is given by the formula:

[ y = mx + b ]

where ( m ) is the slope and ( b ) is the y-intercept. A zero slope means the slope ( m = 0 ), which gives us a horizontal line:

[ y = b ]

This line has the same value for ( y ) regardless of ( x ), meaning it will have infinitely many solutions for any ( x ) value, as long as the equations are consistent.

If you’d like to dive deeper into another topic or have a specific question about solving for ( x ), just let me know!