How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Mathematics

1 answer:

Nina [5.8K]3 years ago

7 0

<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solution
slopes are the same and y-intercepts are different — no solutions
slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at <em>one</em> point, the <em>solution</em>.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence <em>no solutions</em>. If the lines are the same line, they intersect at all points, so there are <em>infinitely many solutions</em>.

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