Factor f(x)= 3x³+5x²-47x+15 into linear factors given that -5 is a zero of f(x)

Explanation:

The left hand side of the first equation is x-3y

The left hand side of the second equation is 2x-6y = 2(x-3y). Note how it's simply double of the first expression x-3y

If we multiply both sides of the first equation by 2, we get

x-3y = 4

2(x-3y) = 2*4

2x-6y = 8

Meaning that 2x-6y = 8 is equivalent to x-3y = 4. Both produce the same line leading to infinitely many solutions. Each solution will lay along the line x-3y = 4.

We can say each solution is in the set {(x,y): x-3y = 4}

Which is the same as saying each solution is of the form (3y+4,y)