if the graph of the equations in a system of linear equations coincide with each other, what does that tell you about the solution of the system? explain

Question

if the graph of the equations in a system of linear equations coincide with each other, what does that tell you about the solution of the system? explain

Answer 1

Hi Bailey--

 

If by "coincide" you mean that the lines intersect, it means that the solution to the system is that intersection point.

 

For example, if the intersection point of the 2 lines is (3,7) on the graph, it means that in both equations, x = 3 and y = 7.

 

If you mean that the 2 equations result in the same line, it means that the 2 equations were actually equivalent, but that one could be simplified to be identical with the other. For example, if you have 2x + 2y = 8 and 4x + 4y = 16, they will give you the same line, and you can see that if you divide that second equation by 2 all the way across, it just becomes the first equation.

 

Hope this helps!

 

Matt in NY