Question

How many solutions does the system have?
x=y-2
-3x+3y=6

Answer 1

Infinitely many solutions.

Explanation:

`\left\{\begin{array}{ccc}x=y-2&(1)\\-3x+3y=6&(2)\end{array}\right\qquad\text{substitute (1) to (2)}\\\\-3(y-2)+3y=6\qquad\text{use the distributive property}\\-3y+6+3y=6\qquad\text{combine like terms}\\(-3y+3y)+6=6\\6=6\qquad\bold{TRUE}\\\\\text{That is why the system of equations has infinitely many solutions.}`