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Question 28690: 4X+7Y=32
4X+2Y=64
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! To solve equations of this kind you have to think of the variable expession 4X (or whatever) as a number. With an equation you can subtract or add a number to both sides of the equation and it still remains true that the two sides are equal. If you saw 2 + 7 = 9 you know you could subtract 2 from each side and end up with 7 = 7. Well, instead of 2 you have something like 4X. That would be 4X + 7Y = 32. Let's subtract the number 7Y from both sides. You get
4X + 7Y - 7Y = 32 - 7Y. This simplifies to 4X + 2Y = 32 - 7Y. Subtract the number 2Y from both sides, giving 4X = 32 - 5Y. Aha! you now know what 4X equals. Since it's the same X and Y in the second equation, which is 4X + 2Y = 64, you can subtract 4X from both sides of the second equation. But here's the trick ... you use 4X when you subtract from the left side of the equation and you use 32 - 5Y when you subtract from the right side of the equation. They are equal, so you can do this. You are subtracting the same number from each side of the second equation.
Doing this you get 4X - 4X = 64 - 32 + 5Y. And that simplifies to
0 = 32 + 5Y. Or, rearranging, 5Y = -32.
If 5 times Y equals -32, then 1 times Y must equal -32/5. [Do you see why?]
Now you can replace Y with its value.
4X + 2Y = 64 becomes  . This is 4X -64/5 = 64.
Dividing both sides by 4 gives X - 16/5 = 16. And X = 16 + 16/5, which is
X = 96/5.
Checking  . Right!
And  . Right!
Of course there is a short cut, once you understand where this came from.
You can subtract the entire left side of the second equation from the left side of the first equation, and the entire right side of the second equation from the right side of the first equation. You get
4X + 7Y - (4X + 2Y) = 32 - 64
4X + 7Y - 4X - 2Y = 32 - 64
5Y = -32
Y = -32/5
This is the same thing, but just hides all the rules being applied to get there. Practice will make this easy.
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