How do you determine whether a linear system has one solution, many solutions, or no solution when given y = 5x - 7 and -4 + y = -1 ?
1 Answer
The one solution, the point where the lines represented by the two equations cross, is the point
Explanation:
These equations are for straight lines. If they cross there will be one solution - the point where they cross. If they are parallel there will be no solutions. If they are the same line there will be many (infinite) solutions.
First step is to get them both into standard form. Standard form for a line is:
The first line given is already in this form:
For the second one, we rearrange to make y the subject:
This is a horizontal line at
Since the other line has a slope of
That means there will be one solution. We can already tell its
So the one solution, the point where the lines cross, is the point
You could also solve or check this by drawing a graph of the two lines and noting where they cross.