*These three cases are illustrated below: The second graph above, "Case 2", shows two distinct lines that are parallel.Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution.You could also write this equation as Y 50 = F, since what you made plus 50 dollars equals what your friend made.*

*These three cases are illustrated below: The second graph above, "Case 2", shows two distinct lines that are parallel.*Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution.You could also write this equation as Y 50 = F, since what you made plus 50 dollars equals what your friend made.

This is called an "inconsistent" system of equations, and it has no solution.

The third graph above, "Case 3", appears to show only one line. These "two" lines, really being the same line, "intersect" at every point along their length.

That means solve for Y; in other words, get Y by itself on the left side of the equals sign.

So subtract F from both sides: To graph the first equation, Y = -F 200, draw a point at (0, 200), and then use the slope to find more points.

When you are solving systems of equations (linear or otherwise), you are, in terms of the equations' related graphed lines, finding any intersection points of those lines.

For two-variable linear systems of equations, there are then three possible types of solutions to the systems, which correspond to three different types of graphs of two straight lines.This is called a "dependent" system, and the "solution" is the whole line.-point), no solution at all, or an infinite solution (being all the solutions to the equation).You will never have a system with two or three solutions; it will always be one, none, or infinitely-many.To graph the second equation, Y = F – 50, use the y-intercept of -50 to draw the first point at (0, -50).Since the slope is 1, start at (0, -50), and then go up one unit and over one unit. Repeat the process starting from (1, -49) and you'll get a third point at (2, -48).Solving them isn't just important for your math grades; it can save you a lot of time whether you're trying to set goals for your business or your sports team.For example, imagine you and your friend are setting up a lemonade stand.Next, you need to graph both equations on the same coordinate plane.Graph your amount, Y, on the y-axis and your friend's amount, F, on the x-axis (it actually doesn't matter which is which as long as you label them correctly).So one way to graph a line given its equation is to just find two points on it and to draw a straight line through them. To graph a line, it is necesasry to find two points that satisfy . Then a smooth curve should be drawn through the zeros accounting for multiple roots and making sure the signs match up (i.e. Luckily the quadratic factors as making the roots and . So picking one point less than and plugging it in will determine whether the graph is above or below the -axis for all on the interval Since is positive, the graph is above the -axis. After synthetic division, the polynomial reduces to .

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