How do you determine whether a linear system has one solution, many solutions, or no solution when given y – 4 = 2x and y – 2x = 4?
1 Answer
The equations of this system are the same line and therefore would have infinite solutions.
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 and y-intercept are the same these equations represent the same line and therefore every point on each line is the same making the solutions infinite.
If only the slope were the same but the y intercept were unique than the lines would be parallel with not common points and no solution.
If the slope and y intercept are both unique the system lines would intersect and have one common point and one solution.
