Final answer:
By finding the slopes of the lines 3x−6y=−5 and 5x−3y=5, which are 1/2 and −(5/3) respectively, we can conclude that the lines are not parallel as their slopes are not identical.
Step-by-step explanation:
To determine if the lines represented by the equations 3x−6y=−5 and 5x−3y=5 are parallel, we need to find their slopes and compare them. For two lines to be parallel, their slopes must be identical, as parallel lines have the same direction and never intersect.
First, let's put both equations into slope-intercept form, which is y = mx + b, where m represents the slope and b the y-intercept.
For the first equation, 3x−6y=−5, we solve for y:
- 3x − 6y = −5
- −6y = −5 − 3x
- y = (−5/6) + (3x/6)
- y = (1/2)x + 5/6
The slope of this line is 1/2.
Now, for the second equation, 5x−3y=5, we also solve for y:
- 5x − 3y = 5
- −3y = 5 − 5x
- y = (5/3) − (5x/3)
- y = −(5/3)x + 5/3
The slope of the second line is −(5/3).
Since the slopes of the two lines are 1/2 and −(5/3) respectively, and these two values are not the same, we can conclude that the lines are not parallel.