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# Chak's Responses in WyzAnt Answers

#### solve by graphing. Tell whether each system has one solution, infinitely many solutions, or no solution. x-2y=3 y=-2x+6

I also need help with other questions.

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Asked by Casey from Miami, FL
10

To solve a system of linear equation graphically, it is best to write both equations in slope-intercept form first. After you put them in slope-intercept form, you should be able to graph them easily.

Now, to determine whether the system one solution, no solution, or infinitely many solution, you will have to see how the graph looks like.

For one solution, the two lines have to intersect at exactly one point, since both equations are satisfied at the intersection.

For no solution, the two lines have to never intersect, which means they have to be parallel lines. In other words, no solution will satisfy both equation.

For infinitely many solutions, the two lines have to overlap each other, which means one equation has to be a multiple of the other equations. When that happens, any point on the line will satisfy the equation, so you will have infinitely many solutions.

Now, for this particular question, if you rewrite the first equation into slope-intercept form, you will get y=1/2x - 3/2. If you put both line on the graph, you will see them intersect at exactly one location, and that will be your solution for the solution. (i.e. one solution)

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