how many solutions does the system of the equation y=5x+7 and y=5x+8 have?


Brian Monetti, I <3 math!

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This system of equations actually has no solutions! This is because there are no X,Y pairs which will solve both equations. You can prove this by setting the equations together. Because the right side of each equation equals Y, we can set them to be equal to each other. We would get: 5x+7 = 5x+8 If you subtract 5x from each side, you get 7=8 which is not true, and thus there is no solution of X,Y which solve the equation.

You can also visualize it by plotting the equations on a graph. These equations both have the same slope of 5, and because their Y intercepts are different (7 and 8 respectively) they will never intersect, and thus there are no solutions. Hope this helps!

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