Question

1.How many solutions does the system of equations have?

y=6x+2

y=6x+4

a. one
b. two
c. infinite
d. none

2. How many solutions does the system of equations have?

y=1/2x-3

x-2y=6

a. one
b. two
c. infinitely many
d. none

3. How many solutions does the system of equations have?

y-6=-3

y-6x=-6

a. one
b. two
c. none
d. infinitely many

I just do not get this at all it would be nice if you could show me how you get this.

Answer 1

get all the equations into slope-intercept form (y = mx + b)

1. the slopes are the same but the intercepts are different
... the lines are parallel
... they never intersect so no solution

2. the slopes are the same and so are the intercepts
... the lines lie on top of each other
... an infinite number of solutions

3. the slopes are different
... the lines intersect
... one solution

Answer 2

Y=6x-10
Y=2(3x-5)

Answer 3

Y=6x-10
Y=2(3x-5)
Tell if the system has one,none,or infinite solutions

Answer 4

Y=-2x+2
Y=-2x-2

Answer 5

Y=3x-2
Y=2(x-1)