Q: When solving a system of equations by graphing how is the solution found?

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A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.

graphing method is when you graph two lines and then find the intersection which is the answer of the system of equations

The required solution may not be within the range that is plotted, and you would have to start all over again.

Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).

You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.

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Graph both equations on the same graph. Where they intersect is the solution to the system of equations

The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra. The main disadvantage is that your answer will be approximate due to having to read the answer from a graph. Where the solution are integer values, this might be alright, but if you are looking for an accurate decimal answer, this might not be able to be achieved. Another disadvantage to solving linear equations by graphing is that at most you can have two unknown variables (assuming that you are drawing the graph by hand).

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A system of linear equations is consistent if there is only one solution for the system. Thus, if you see that the drawn lines intersect, you can say that the system is consistent, and the point of intersection is the only solution for the system. A system of linear equations is inconsistent if it does not have any solution. Thus, if you see that the drawn lines are parallel, you can say that the system is inconsistent, and there is not any solution for the system.

you cannot determine the exact value of the point

You see the point the two lines cross, if they do. This is the solution to the system since it is the values of (x,y) that are on both lines The solution is a sytems is those points, if any, (x,y) that satisfy both equations. That is the same as saying they are on both lines. If you graph the equations, this is the same as saying the points that are in the intersection of the lines. This is why parallel lines represent a system with no solution and if two equations are the same line there is an infinite number of solutions.

graphing method is when you graph two lines and then find the intersection which is the answer of the system of equations

The required solution may not be within the range that is plotted, and you would have to start all over again.

If you graph the two functions defined by the two equations of the system, and their graphs are two parallel line, then the system has no solution (there is not a point of intersection).

Yes you can, if the solution or solutions is/are real. -- Draw the graphs of both equations on the same coordinate space on the same piece of graph paper. -- Any point that's on both graphs, i.e. where they cross, is a solution of the system of equations. -- If both equations are linear, then there can't be more than one such point.

Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).

You find a solution set. Depending on whether the equations are linear or otherwise, consistent or not, the solution set may consist of none, one, several or infinitely many possible solutions to the system.