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Question 115258: How do you work substitution equations?
ex.
t=0.2s+10
4s+5t=35
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! If you have two unknowns you need two equations independent equations to solve for the two unknowns.
There are several ways you can work the two equations to solve for the two unknowns.
For example, you can graph them and find out where the graphs cross. Or you can subtract them
such that one of the variables drops out. Or you can use variable substitution.
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You have asked about variable substitution. And here's how you can do it.
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In one of the two equations you need to solve for one of the variables in terms of the other.
This has already been done for you. Notice that in the top equation you are told that t equals
0.2s + 10. This means that you can replace t by 0.2s + 10 because they are equals.
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So go to the second equation:
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4s + 5t = 35
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and replace t with 0.2s + 10. When you do that replacement the second equation becomes:
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4s + 5(0.2s +10) = 35
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Do the multiplication on the left side and the equation becomes:
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4s + s + 50 = 35
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Combine the two "s" terms on the left side and you have:
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5s + 50 = 35
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Get rid of the 50 on the left side by subtracting 50 from both sides to get:
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5s = -15
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Solve for s by dividing both sides by 5 and you have:
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s = -15/5 = -3
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Now that you know one of the variables, you can find the other variable. You do that by
returning to either of the two original equations and substituting -3 for s. For example, return
to the top equation that said:
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t = 0.2s + 10
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substitute -3 for s and this equation becomes:
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t = 0.2(-3) + 10
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Do the multiplication on the right side and you have:
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t = -0.6 + 10
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and combine the two terms on the right side to get:
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t = 9.4
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Hope this example helps you to understand the process of substitution.
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