 So now we know how to do a whole bunch of different kinds of systems and how do we decide which way we want to do it? Well, let's look at these examples If you look at this system, we have a y equal equation and that is always Set up perfectly for substitution. Now graphing could be done here But we'd have to use our shortcut and then when we divide by 4 to put it in our calculator remember It's negative 26 minus 3x All over 4 so that's a little bit harder Substitution is probably the easiest way to solve this one in the second system We can see that we have a coefficient of 1 on this x so because of that Substitution would be very nice. We could easily say that x is equal to 12 minus 3 y It wouldn't be difficult though to also do elimination We would just have to multiply this equation by positive 5 and then we would have 5x plus 15 y equal to 60 and We could add the two equations Either one would be probably just as simple as the other one in this case and this last example You can see that there's no coefficient of 1 So that doesn't make Substitution work very nicely, but elimination would work very nicely here Get the coefficients like we want them to be and then add the two equations graphing again would be a little more difficult because of these coefficients any System can be solved any of the three ways, but if you look closely you might find that one's a little easier than the other