# 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)

answered Mar 25, 2012 by Level 5 User (10,220 points)

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