Let x= truck

Actually, x is the number of round trips made by the 10 ton truck and y is the number of round trips made by the 12 ton truck.

x + y = 20

We know from the problem that if you add together the number of round trips made by each truck, you get the 20 trip total.

x= 20-y

This is just math to isolate x. So, now we can substitute "20-y" for x in the equation and it will be easier to solve.

10 (20-y) + 12y = 226

This equation reflects how much topsoil each truck carried. Truck x (which is '20-y' now) carried 10 tons on each of its round trips, and truck y carried 12 tons per trip. [Note that even though it's a round trip, they only carried soil in one direction.]

200-10y + 12y = 226

This step and the ones that follow are just math steps to simplify the equation. This one turns 10(20-y) into 200 - 10y

2(100-5y+6y)=226

This is one way to further simplify by pulling 2 out from each part of the left hand side.

2(100+y) = 226

This is just showing that -5y + 6y is the same as 1y or just y

100 + y = 113

y= 13

x = 7

Actually, x is the number of round trips made by the 10 ton truck and y is the number of round trips made by the 12 ton truck.

x + y = 20

We know from the problem that if you add together the number of round trips made by each truck, you get the 20 trip total.

x= 20-y

This is just math to isolate x. So, now we can substitute "20-y" for x in the equation and it will be easier to solve.

10 (20-y) + 12y = 226

This equation reflects how much topsoil each truck carried. Truck x (which is '20-y' now) carried 10 tons on each of its round trips, and truck y carried 12 tons per trip. [Note that even though it's a round trip, they only carried soil in one direction.]

200-10y + 12y = 226

This step and the ones that follow are just math steps to simplify the equation. This one turns 10(20-y) into 200 - 10y

2(100-5y+6y)=226

This is one way to further simplify by pulling 2 out from each part of the left hand side.

2(100+y) = 226

This is just showing that -5y + 6y is the same as 1y or just y

100 + y = 113

y= 13

x = 7