Question

For questions 3–6, how many solutions does each system have?

3. –4y = x – 4
y = –1/4 x + 1
(1 point)
one
two
infinite
none
4. y = 6x + 2

y = 6x + 4 (1 point)
one
two
infinite
none
5. y = 1/2 x – 3
x – 2y = 6
(1 point)
one
two
infinite
none
6. y – 5x = –6

y – 5x = –4 (1 point)
one
two
infinite
none

Answer 1

Rewrite your equations in y = mx + b form and then ask yourself the following questions:

Are the slopes different? (If so, then the lines will intersect at one point).

Are the slopes the same? If so, are the y-intercepts identical? If yes to both questions, then you have two identical lines and so they overlap and have infinite solutions.

If the slopes are the same but the lines have different y-intercepts then you have two parallel lines that never intersect.