Question

Y=1/4x+1

y=1/4x-1
How many solutions does this system
of equations have?
One solution, because the slopes
are different.
No solution, because the slopes
are the same and the y-intercepts
are different.
Infinitely many solutions, because
the slopes are the same and the
y-intercepts are the same.

Answer 1

No solution, because the slopes are the same and the y-intercepts are different.

Explanation:

The two equations are:

y = 1/4x + 1 and y= 1/4x - 1

Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1

1/4x cancels out of the equation and we get the absurdity:

1 = -1

This indicates no solution to the system of equations

Answer:
No solution, because the slopes are the same and the y-intercepts are different.

We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)