Question

wrap-up questions

1. what does a solution to a system of equations look like on the graph?
2. will a system of two linear equations always have a solution?
3. if two linear equations are parallel, how many solutions will there be?
4. if two linear functions have the exact same slope and y-intercept, how many solutions will there be?

Explanation:

1. A system's solution is the point(s) where all graphs intersect, as this point satisfies all equations in the system.
2. A system of two linear equations can have no solution (parallel lines) so it does not always have a solution.
3. Parallel lines never intersect, so there are no points that satisfy both equations.
4. If two linear functions share the exact same slope and y-intercept, they are the identical line, meaning every point on the line is a solution.

Answer:

1. It is the point (or points) where all the graphs of the equations in the system intersect.
2. No, a system of two linear equations will not always have a solution.
3. There will be 0 solutions.
4. There will be infinitely many solutions.