You know by the Pythagorean theorem that a2 +b2 = c2 where a and b are the legs of the triangle and c is the hypotenuse or longest side. When they say the other two legs are consecutive integers, that means that x = x+1 or in this case c = b+1. By substituting c = b+1 and 7cm into...

This is a classic two equations with two unknowns type problem. The goal in the first step is to eliminate one of the variables by making an equivalent statement in terms of one variable. In order to get rid of one of the variables, substitute either
y = 2-x or ...

By the order of operations, multiplication comes before addition. The (x-2y+6z) is being mulitplied by -1, so distribute that through first. Then remember that addition is commutative and you can add/subtract like terms together, for example 3y + 4y = 7y.