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how can you solve system of equations by graphing?

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Each equation represents a line on a graph (for 2 dimensions). The solution you are searching for is the intersection of the lines. There are three possible outcomes: 1) The lines intersect and the corresponding x,y coordinates are the solution to the system of equations. 2) The lines are parallel and the system is what we call inconsistent meaning there is no solution. 3) Lastly the equations could represent the exact same line, which means that they intersect everywhere and the solution is the entire line.

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So if you have a system of equations each equation can be used to represent a line. For example the equation 2x+4y=4 is equivalent to x = -2y+2 which represents a line of slope -2 and intercepts the x-axis at 2. So we can plot that line. If we take the next equation, lets say x=y+2. So here there is a slope of 1 and it also intercepts the x-axis at 2. On a graph we would see that that the two lines meet at x=2 and y=0, that is the solution.

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