document.write( "Question 91747: please can you help with this problem -3x+2y=8 3x+2y=8 university of phoenix elementary and intermidiate algebra \n" ); document.write( "
Algebra.Com's Answer #66628 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Lets solve this system using substitution\r
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Solved by pluggable solver: Solving a linear system of equations by subsitution

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\n" ); document.write( " Lets start with the given system of linear equations
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\n" ); document.write( " \"-3%2Ax%2B2%2Ay=8\"
\n" ); document.write( " \"3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.
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\n" ); document.write( " Solve for y for the first equation
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\n" ); document.write( " \"2%2Ay=8%2B3%2Ax\"Add \"3%2Ax\" to both sides
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\n" ); document.write( " \"y=%288%2B3%2Ax%29%2F2\" Divide both sides by 2.
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\n" ); document.write( " Which breaks down and reduces to
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\n" ); document.write( " \"y=4%2B%283%2F2%29%2Ax\" Now we've fully isolated y
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\n" ); document.write( " Since y equals \"4%2B%283%2F2%29%2Ax\" we can substitute the expression \"4%2B%283%2F2%29%2Ax\" into y of the 2nd equation. This will eliminate y so we can solve for x.
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\n" ); document.write( " \"3%2Ax%2B2%2Ahighlight%28%284%2B%283%2F2%29%2Ax%29%29=8\" Replace y with \"4%2B%283%2F2%29%2Ax\". Since this eliminates y, we can now solve for x.
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\n" ); document.write( " \"3%2Ax%2B2%2A%284%29%2B2%283%2F2%29x=8\" Distribute 2 to \"4%2B%283%2F2%29%2Ax\"
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\n" ); document.write( " \"3%2Ax%2B8%2B%286%2F2%29%2Ax=8\" Multiply
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\n" ); document.write( " \"3%2Ax%2B8%2B3%2Ax=8\" Reduce any fractions
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\n" ); document.write( " \"3%2Ax%2B3%2Ax=8-8\" Subtract \"8\" from both sides
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\n" ); document.write( " \"3%2Ax%2B3%2Ax=0\" Combine the terms on the right side
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\n" ); document.write( " \"6%2Ax=0\" Now combine the terms on the left side.
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\n" ); document.write( " \"cross%28%281%2F6%29%286%2F1%29%29x=%280%2F1%29%281%2F6%29\" Multiply both sides by \"1%2F6\". This will cancel out \"6%2F1\" and isolate x
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\n" ); document.write( " So when we multiply \"0%2F1\" and \"1%2F6\" (and simplify) we get
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\n" ); document.write( " \"x=0\" <---------------------------------One answer
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\n" ); document.write( " Now that we know that \"x=0\", lets substitute that in for x to solve for y
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\n" ); document.write( " \"3%280%29%2B2%2Ay=8\" Plug in \"x=0\" into the 2nd equation
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\n" ); document.write( " \"0%2B2%2Ay=8\" Multiply
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\n" ); document.write( " \"2%2Ay=8%2B0\"Add \"0\" to both sides
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\n" ); document.write( " \"2%2Ay=8\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F2%29%282%29%29%2Ay=%288%2F1%29%281%2F2%29\" Multiply both sides by \"1%2F2\". This will cancel out 2 on the left side.
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\n" ); document.write( " \"y=8%2F2\" Multiply the terms on the right side
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\n" ); document.write( " \"y=4\" Reduce
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\n" ); document.write( " So this is the other answer
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\n" ); document.write( " \"y=4\"<---------------------------------Other answer
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\n" ); document.write( " So our solution is
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\n" ); document.write( " \"x=0\" and \"y=4\"
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\n" ); document.write( " which can also look like
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\n" ); document.write( " (\"0\",\"4\")
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\n" ); document.write( " Notice if we graph the equations (if you need help with graphing, check out this solver)
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\n" ); document.write( " \"-3%2Ax%2B2%2Ay=8\"
\n" ); document.write( " \"3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " we get
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\n" ); document.write( " graph of \"-3%2Ax%2B2%2Ay=8\" (red) and \"3%2Ax%2B2%2Ay=8\" (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.
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\n" ); document.write( " and we can see that the two equations intersect at (\"0\",\"4\"). This verifies our answer.
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\n" ); document.write( " Check:
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\n" ); document.write( " Plug in (\"0\",\"4\") into the system of equations
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\n" ); document.write( " Let \"x=0\" and \"y=4\". Now plug those values into the equation \"-3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " \"-3%2A%280%29%2B2%2A%284%29=8\" Plug in \"x=0\" and \"y=4\"
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\n" ); document.write( " \"0%2B8=8\" Multiply
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\n" ); document.write( " \"8=8\" Add
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\n" ); document.write( " \"8=8\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"0\",\"4\") satisfies \"-3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " Let \"x=0\" and \"y=4\". Now plug those values into the equation \"3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " \"3%2A%280%29%2B2%2A%284%29=8\" Plug in \"x=0\" and \"y=4\"
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\n" ); document.write( "
\n" ); document.write( " \"0%2B8=8\" Multiply
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\n" ); document.write( " \"8=8\" Add
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\n" ); document.write( " \"8=8\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"0\",\"4\") satisfies \"3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " Since the solution (\"0\",\"4\") satisfies the system of equations
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\n" ); document.write( " \"-3%2Ax%2B2%2Ay=8\"
\n" ); document.write( " \"3%2Ax%2B2%2Ay=8\"
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\n" ); document.write( " this verifies our answer.
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