x - 6y = 30, [1]
2x - 5y = 30 [2]
To solve by substitution you need to rearrange one of the equations. So take equation [1] :
x - 6y = 30
Then add 6y to both sides of the equation:
x - 6y + 6y = 30 + 6y
x = 30 + 6y
So now put this equation into equation [2] :
2x - 5y = 30
2(30 + 6y) - 5y = 30
So now multiply out the brackets:
(2 x 30) + (6y x 2) - 5y = 30
60 + 12y - 5y = 30
60 + 7y = 30
Now you can subtract 60 from both sides of the equation:
60 + 7y - 60 = 30 - 60
7y = - 30
Now divide both sides of the equation by 7:
7y / 7 = -30 / 7
y = -30 / 7
And so now you can put this solution into one of the original equations to find the solution for x :
x - 6y = 30
x - 6(-30/7) = 30
x + (6 x 30) / 7 = 30
x + 180 / 7 = 30
Subtract 180/7 by both sides of the equation:
x + 180/7 - 180/7 = 30 - 180/7
x = 30 - 180/7
You can now put the answer all over the same fraction:
x = 30(7/7) - 180/7 = (30 x 7)/7 - 180/7 = 210/7 - 180/7 = (210-180)/7 = 30/7
This means that the solution to this system of equations is:
(30/7, -30/7) 