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
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,
Rearrange the two equations into slope intercept form of
where m = slope and b = y intercept
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.
