document.write( "Question 115258: How do you work substitution equations?\r
\n" ); document.write( "\n" ); document.write( "ex. \r
\n" ); document.write( "\n" ); document.write( "t=0.2s+10
\n" ); document.write( "4s+5t=35 \n" ); document.write( "
Algebra.Com's Answer #83838 by bucky(2189)\"\" \"About 
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.
\n" ); document.write( "There are several ways you can work the two equations to solve for the two unknowns.
\n" ); document.write( "For example, you can graph them and find out where the graphs cross. Or you can subtract them
\n" ); document.write( "such that one of the variables drops out. Or you can use variable substitution.
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\n" ); document.write( "You have asked about variable substitution. And here's how you can do it.
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\n" ); document.write( "In one of the two equations you need to solve for one of the variables in terms of the other.
\n" ); document.write( "This has already been done for you. Notice that in the top equation you are told that t equals
\n" ); document.write( "0.2s + 10. This means that you can replace t by 0.2s + 10 because they are equals.
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\n" ); document.write( "So go to the second equation:
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\n" ); document.write( "4s + 5t = 35
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\n" ); document.write( "and replace t with 0.2s + 10. When you do that replacement the second equation becomes:
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\n" ); document.write( "4s + 5(0.2s +10) = 35
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\n" ); document.write( "Do the multiplication on the left side and the equation becomes:
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\n" ); document.write( "4s + s + 50 = 35
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\n" ); document.write( "Combine the two \"s\" terms on the left side and you have:
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\n" ); document.write( "5s + 50 = 35
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\n" ); document.write( "Get rid of the 50 on the left side by subtracting 50 from both sides to get:
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\n" ); document.write( "5s = -15
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\n" ); document.write( "Solve for s by dividing both sides by 5 and you have:
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\n" ); document.write( "s = -15/5 = -3
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\n" ); document.write( "Now that you know one of the variables, you can find the other variable. You do that by
\n" ); document.write( "returning to either of the two original equations and substituting -3 for s. For example, return
\n" ); document.write( "to the top equation that said:
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\n" ); document.write( "t = 0.2s + 10
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\n" ); document.write( "substitute -3 for s and this equation becomes:
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\n" ); document.write( "t = 0.2(-3) + 10
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\n" ); document.write( "Do the multiplication on the right side and you have:
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\n" ); document.write( "t = -0.6 + 10
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\n" ); document.write( "and combine the two terms on the right side to get:
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\n" ); document.write( "t = 9.4
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\n" ); document.write( "Hope this example helps you to understand the process of substitution.
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