How do you determine whether a linear system has one solution, many solutions, or no solution when given -5x+3y= -5 and y= 5/3x + 1?

1 Answer
Oct 20, 2015

These equations represent parallel lines and have not common points of intersection of solution.

Explanation:

In order to determine the solutions possibilities of the system of equations,

#-5x-3y=-5 and y=5/3x+4#

Rearrange the two equations into slope intercept form of #y=mx+b#
where m = slope and b = y intercept

#-5x-3y=-5# becomes #y=5/3x+5/3# #m=2 and b=5/3#
#y=5/3x+4# becomes #y=5/3x+4# #m=5/3 and b=4#

Since the slope is the same for each equations and the y-intercepts are different for these equations the graphs of these lines are parallel and have no common points of solution.

If only the slope were the same and the y intercept were the same than the lines would be the same line and would have infinite solutions.

If the slope and y intercept are both unique the system lines would intersect and have one common point and one solution.