Determine whether the system of equations

has one solution, no solution, or infinitely
many solutions.
1. y - 13 = 5x
y - 5x = 12
2. y= 2x + 10
3 y - 6x = 30
4.y= 1/4x = -1
y - 2=4×

1 answer

look at the equations in slope-intercept form:
y = 5x+13
y = 5x+12
Clearly, no value of x can make both of them the same.

Try this with the others. If the slopes are different, there will always be a solution, since the lines are not parallel.