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identify the number of solutions for the systems 2y=4x+2 y+3=2x



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Christopher G. | Math Tutor - Algebra, Trig, Calculus, SAT/ACT MathMath Tutor - Algebra, Trig, Calculus, SA...
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2y = 4x + 2     I'll call this equation A

y + 3 = 2x       and this equation B

I would first simplify both equations so that they are in y = mx + b form. I will do this by dividing out 2 from each term in equation A and by subtracting 3 from both sides in equation B.

2y = 4x + 2     ->     y = 2x + 1

y + 3 = 2x     ->     y = 2x - 3

Now we can see that both equations have a slope of 2. When two lines' slopes are equal, then they are parallel. Since they are not the same line (which would mean they would have the same slope and y-intercept), they do not intersect, and so there are no solutions for this system.