document.write( "Question 111901: what is the solution to- 9x-3y=3
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Algebra.Com's Answer #81663 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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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( " \"9%2Ax-3%2Ay=3\"
\n" ); document.write( " \"3%2Ax%2B8%2Ay=-17\"
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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( " \"-3%2Ay=3-9%2Ax\"Subtract \"9%2Ax\" from both sides
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\n" ); document.write( " \"y=%283-9%2Ax%29%2F-3\" Divide both sides by -3.
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\n" ); document.write( " Which breaks down and reduces to
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\n" ); document.write( " \"y=-1%2B3%2Ax\" Now we've fully isolated y
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\n" ); document.write( " Since y equals \"-1%2B3%2Ax\" we can substitute the expression \"-1%2B3%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%2B8%2Ahighlight%28%28-1%2B3%2Ax%29%29=-17\" Replace y with \"-1%2B3%2Ax\". Since this eliminates y, we can now solve for x.
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\n" ); document.write( " \"3%2Ax%2B8%2A%28-1%29%2B8%283%29x=-17\" Distribute 8 to \"-1%2B3%2Ax\"
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\n" ); document.write( " \"3%2Ax-8%2B24%2Ax=-17\" Multiply
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\n" ); document.write( " \"3%2Ax-8%2B24%2Ax=-17\" Reduce any fractions
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\n" ); document.write( " \"3%2Ax%2B24%2Ax=-17%2B8\"Add \"8\" to both sides
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\n" ); document.write( " \"3%2Ax%2B24%2Ax=-9\" Combine the terms on the right side
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\n" ); document.write( " \"27%2Ax=-9\" Now combine the terms on the left side.
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\n" ); document.write( " \"cross%28%281%2F27%29%2827%2F1%29%29x=%28-9%2F1%29%281%2F27%29\" Multiply both sides by \"1%2F27\". This will cancel out \"27%2F1\" and isolate x
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\n" ); document.write( " So when we multiply \"-9%2F1\" and \"1%2F27\" (and simplify) we get
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\n" ); document.write( " \"x=-1%2F3\" <---------------------------------One answer
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\n" ); document.write( " Now that we know that \"x=-1%2F3\", lets substitute that in for x to solve for y
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\n" ); document.write( " \"3%28-1%2F3%29%2B8%2Ay=-17\" Plug in \"x=-1%2F3\" into the 2nd equation
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\n" ); document.write( " \"-1%2B8%2Ay=-17\" Multiply
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\n" ); document.write( " \"8%2Ay=-17%2B1\"Add \"1\" to both sides
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\n" ); document.write( " \"8%2Ay=-16\" Combine the terms on the right side
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\n" ); document.write( " \"cross%28%281%2F8%29%288%29%29%2Ay=%28-16%2F1%29%281%2F8%29\" Multiply both sides by \"1%2F8\". This will cancel out 8 on the left side.
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\n" ); document.write( " \"y=-16%2F8\" Multiply the terms on the right side
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\n" ); document.write( " \"y=-2\" Reduce
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\n" ); document.write( " So this is the other answer
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\n" ); document.write( " \"y=-2\"<---------------------------------Other answer
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\n" ); document.write( " So our solution is
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\n" ); document.write( " \"x=-1%2F3\" and \"y=-2\"
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\n" ); document.write( " which can also look like
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\n" ); document.write( " (\"-1%2F3\",\"-2\")
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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( " \"9%2Ax-3%2Ay=3\"
\n" ); document.write( " \"3%2Ax%2B8%2Ay=-17\"
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\n" ); document.write( " we get
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\n" ); document.write( " graph of \"9%2Ax-3%2Ay=3\" (red) and \"3%2Ax%2B8%2Ay=-17\" (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 (\"-1%2F3\",\"-2\"). This verifies our answer.
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\n" ); document.write( " Check:
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\n" ); document.write( " Plug in (\"-1%2F3\",\"-2\") into the system of equations
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\n" ); document.write( " Let \"x=-1%2F3\" and \"y=-2\". Now plug those values into the equation \"9%2Ax-3%2Ay=3\"
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\n" ); document.write( " \"9%2A%28-1%2F3%29-3%2A%28-2%29=3\" Plug in \"x=-1%2F3\" and \"y=-2\"
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\n" ); document.write( " \"-9%2F3%2B6=3\" Multiply
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\n" ); document.write( " \"9%2F3=3\" Add
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\n" ); document.write( " \"3=3\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"-1%2F3\",\"-2\") satisfies \"9%2Ax-3%2Ay=3\"
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\n" ); document.write( " Let \"x=-1%2F3\" and \"y=-2\". Now plug those values into the equation \"3%2Ax%2B8%2Ay=-17\"
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\n" ); document.write( " \"3%2A%28-1%2F3%29%2B8%2A%28-2%29=-17\" Plug in \"x=-1%2F3\" and \"y=-2\"
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\n" ); document.write( " \"-3%2F3-16=-17\" Multiply
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\n" ); document.write( " \"-51%2F3=-17\" Add
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\n" ); document.write( " \"-17=-17\" Reduce. Since this equation is true the solution works.
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\n" ); document.write( " So the solution (\"-1%2F3\",\"-2\") satisfies \"3%2Ax%2B8%2Ay=-17\"
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\n" ); document.write( " Since the solution (\"-1%2F3\",\"-2\") satisfies the system of equations
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\n" ); document.write( " \"9%2Ax-3%2Ay=3\"
\n" ); document.write( " \"3%2Ax%2B8%2Ay=-17\"
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\n" ); document.write( " this verifies our answer.
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