What does it mean for a system to have infinite solutions? What do the graphs of a system of infinite solutions look like? Explains what it means graphically to have infinite solutions
A system of equations has infinite solutions when the equations are dependent on each other and can be written as multiples of one another. This means that there are an infinite number of possible values for the variables that would satisfy all of the equations in the system.
Graphically, a system of equations with infinite solutions would result in parallel lines or overlapping lines. This is because the equations in the system are essentially describing the same line or lines with the same slope and y-intercept. When plotted on a graph, the lines would coincide with each other, indicating that there are an infinite number of points where the lines intersect and the system is satisfied.
In summary, a system of equations has infinite solutions when the equations are linearly dependent, resulting in parallel or overlapping lines on a graph. This means that there are infinitely many points that satisfy all of the equations in the system.