Since neither equation has a variable with a coefficient of 1, the Substitution Method may not be the easiest. Instead, let's use the Elimination Method. To use this method, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other equation. This means that either the x-terms or the y-terms must cancel each other out.
3 x-3 y=-2 & (I) -6 x+6 y=4 & (II)
Currently, none of the terms in this system will cancel out. Therefore, we need to find a common multiple between two variable like terms in the system. If we multiply (I) by 2, both the x-terms and the y-terms will have opposite coefficients.
2(3 x-3 y)=2(-2) -6 x+6 y)=4 ⇒ 6x- 6y=-4 - 6x+ 6y=4
We can see that both the x-terms and the y-terms will eliminate each other if we add (I) to (II).
Solving this system of equations resulted in an identity; 0 is always equal to itself. This means that the lines are the same and have infinitely many intersection points. Therefore, the system has infinitely many solutions.
