Solve the system of equations: 12x + 6y = 60 and 3y = -6x + 30 a) (10,0) b) (0,10) c) infinite solutions d) no solutions

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