The graphs of the equations y = 5x - 4 and y = 5x + 2 are parallel lines with the same slope of 5 but different y-intercepts. These lines never intersect, which means the system has infinite solutions.
Having infinite solutions means that any point that lies on one of the lines will also lie on the other line. This is because the two equations are equivalent, with the only difference being the y-intercept.
Graphically, having infinite solutions means that the lines representing the equations will overlap each other perfectly, essentially forming a single line. This shows that there are an infinite number of points that satisfy both equations, since any point on one line will also be on the other.
Consider the two equations you circled, which form a system with infinite solutions. Graph them together on the following coordinate grid.
y = 5x - 4 and y = 5x + 2
What do you notice about these graphs? What does it mean for a system to have infinite solutions? What do the graphs of a system with infinite solutions look like? Explain what it means graphically to have infinite solutions.
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