Hello there!
12x + 6y = 60
3y = -6x + 30
Ok so we need to solve 12x + 6y = 60 for x
Let's start by adding -6y to both sides
12x + 6y - 6y = 60 - 6y
12x = -6y + 60
Since we are looking for x, we need to divide both sides by 12
12x/12 = (-6y + 60)/12
x = -1/2 y + 5
We are not done yet, now we need to substitute -1/2 y + 5 for x in 3y = -6x + 30
3y= -6x + 30
3y = -6(-1/2 y + 5)+ 30
3y = 3y
Finally subtracting 3y from both sides
3y - 3y = 3y - 3y
0 = 0
Thus, Infinite Solutions
