math HELP:D plzz?

Question

express each equation in slope intercept form then determine eithout solving wether it has one solution none or infinate.
-x+2y=4
-4xminus2y=-14

Does the system of equation have no solution one or many? explain how YOU can tell without graphing.please.

y=xminus2

6y=3x+7

Answer 1

the way to tell how many solutions it has is by doing

(b^2-4ac)

if it = 0, there's 1
>1, there's 2
<1, there's no real solutions

Answer 2

- x + 2y = 4
- 4x - 2y = - 14

2y = x + 4
2y = - 4x + 14

y = (1/2)x + 2
y = - 2x + 7

The lines are orthogonal, having 1 solution.

y = x - 2
6y = 3x + 7

y = x - 2
y = (1/2)x + 7/6

Because the slopes differ, there is one solution.
(Equal slopes with unequal intercepts would have no solution. Equal slopes with equal intercepts are colinear, with infinite solutions.)