SOLUTION: I am trying to solve a system by substitution. Can you please show me how to solve this? 27y = 3x + 3 5y - 4x = 8 Thank you, Brandon

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Question 23653: I am trying to solve a system by substitution. Can you please show me how to solve this?
27y = 3x + 3
5y - 4x = 8
Thank you,
Brandon
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The substitution method always involves solving one of the equations for one of the variables in terms of the other one. It will help if you divide both sides of the first equation by 3:

9y = x+1
Next subtract 1 from each side in order to solve for x:
9y-1 = x
x= 9y-1

Substitute this into the second equation:
5y -4x = 8
5y - 4(_____) = 8
5y - 4(9y -1) = 8
5y -36 y + 4 = 8
-31y = 4
y = -4/31 (That's pretty ugly!)

x= 9y-1
x=9*(-4/31) -1
x= -36/31 - 31/31
x= -67/31 (That's ugly too!!)

Check in the second equation, especially since the answer is so ugly!
5y - 4x = 8
5(-4/31) -4(-67/31) = 8
-20/31 + 268/31=8
248/31 =8
8=8
It checks after all!!

R^2 at SCC

Substitute this value of y into the x= equation: