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Question 173015: My question is how to do substitution. I am extremely confused because with it because my teacher will not explain it well no matter what.
As an example, questions like these:
y=5-4*x
3*x-2*y=12
Please help and possibly explain in detail how to solve these problems.
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! Hope these additional comments help.
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y=5-4x
Now replace y with(5-4x) in the other equation below & solve for x.
3x-2y=12
3x-2(5-4x)=12 multiply 2(5-4x)
3x-10+8x=12 add (3x8x, add 10 to both sides of the equation)
11x=12+10 add the (12+10)
11x=22 (now divide both sides by 11)
x=22/11 (divide 22 by 11)
x=2 ans. (now substitute 2 for x in the first equation & solve for y)
y=5-4*2 (multiply -4*2)
y=5-8 (subtract 8 from 5)
y=-3 ans.
Proof: (replace x with 2 & y with -3 & solve the equation)
3*2-2*-3=12
6+6=12
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! y=5-4*x
3*x-2*y=12
:
You can write it like this
y = 5 - 4x
3x - 2y = 12
;
Look at the 1st equation; that means that any place you see y, you can substitute
(5-4x) for it
:
In the 2nd equation (3x - 2y = 12), we can substitute (5-4x) for y, so we have
3x - 2(5-4x) = 12
That gives just one unknown (x), which is easy to solve with basic algebra:
:
multiply what's inside the brackets by -2 and you have:
:
3x - 10 + 8x = 12; note that a minus times a minus is plus
:
Perform the necessary operations to get the variables on the left, numbers on the right
3x + 8x = 12 + 10; added 10 to both sides
:
11x = 22
x =  ; divided both sides by 11
x = 2
:
Now substitute 2 for x in the 1st original equation and find y:
y = 5 - 4x
y = 5 - 4(2)
y = 5 - 8
y = -3
;
Check by substituting both solution for x and y in the 2nd equation
3x - 2y = 12
3(2) - 2(-3) = 12
6 + 6 = 12; which is true. (remember minus times a minus is a plus)
:
How about this, did it make sense to you, now?
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