Answer:
Second option
Step-by-step explanation:
For a system of linear equations, there are three possible number of solutions:
Infinite solutions: When the equations are equivalent
One solution: When they are not parallel
No solution: When they are parallel and have different y-intercepts
(When the slope is the same, equations are parallel)
Rearrange equations to slope-intercept form y=mx+b where "m" is slope and "b" is y-intercept. Isolate "y" to do this.
First option:
5x + 5y = 10
5y = -5x + 10
y = -x + 2
2x + 2y = 4
2y = -2x + 4
y = -x + 2
The equations are equivalent. Infinite solutions.
Second option:
3x - 6y = 4
-6y = -3x + 4
y = 1/2 x - 2/3
-4x + 8y = 7
8y = 4x + 7
y = 1/2 x + 7/8
Same slope, different y-intercepts. No solutions.
Third option:
6x + 2y = 6
2y = -6x + 6
y = -3x + 3
7x + 3y = 9
3y = -7x + 9
y = -7/3 x + 3
Different slopes. One solution.
Last option:
3x - 4y = 16
-4y = -3x + 16
y = 3/4 x - 4
2x + 3y = 5
3y = -2x + 5
y = -2/3 x + 5/3
Different slopes. One solution.
