Question 23285: please help me solve this problem: find 3 possible answers to 2x+4y=8
Answer by smik(40)   (Show Source):
You can put this solution on YOUR website! Good question.
Well, what we can do first is set x to zero, and solve for y. In other words, we're wondering what y would have to be if x were 0. So:
2(0) + 4y = 8 (since 2(0) is 0, we can exclude that)
4y = 8 (we divide both sides by 4)
y = 2 (So, when x = 0, y = 2)
Now that we've got one answer. We can set y equal to 0. So:
2x + 4(0) = 8 (since 4(0) is 0, we can exclude that)
2x = 8 (we divide both sides by 2)
x = 4 (When y = 0, x = 4)
Now we've got two answers. We need to find one more answer. An easy way to do this is to set x (or y) to any random value, then shift it to the other side, and solve for y (or x). For this case, let's set x equal to 2 and solve for y. So:
2(2) + 4y = 8
4 + 4y = 8 (Now we can shift the 4 on the left to the right by subtracting it from both sides)
4y = 4 (Divide both sides by 4)
y = 1 (When x = 2, y = 1)
There you go, we've got three answers now. Of course, you could go on and find tonnes of other answers by setting any of the variables to a random value and then solving for the other variable.
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