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document.write( " Lets start with the given system of linear equations \n" );
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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. \n" );
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document.write( " Solve for y for the first equation \n" );
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document.write( " Subtract from both sides \n" );
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document.write( " Divide both sides by 3. \n" );
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document.write( " Which breaks down and reduces to \n" );
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document.write( " Now we've fully isolated y \n" );
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document.write( " Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x. \n" );
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document.write( " Replace y with . Since this eliminates y, we can now solve for x. \n" );
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document.write( " Distribute -1 to  \n" );
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document.write( " Multiply \n" );
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document.write( " Reduce any fractions \n" );
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document.write( " Add to both sides \n" );
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document.write( " Combine the terms on the right side \n" );
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document.write( " Make 4 into a fraction with a denominator of 3 \n" );
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document.write( " Now combine the terms on the left side. \n" );
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document.write( " Multiply both sides by . This will cancel out and isolate x \n" );
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document.write( " So when we multiply and (and simplify) we get \n" );
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document.write( " <---------------------------------One answer \n" );
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document.write( " Now that we know that , lets substitute that in for x to solve for y \n" );
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document.write( " Plug in into the 2nd equation \n" );
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document.write( " Multiply \n" );
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document.write( " Add to both sides \n" );
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document.write( " Combine the terms on the right side \n" );
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document.write( " Multiply both sides by . This will cancel out -1 on the left side. \n" );
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document.write( " Multiply the terms on the right side \n" );
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document.write( " Reduce \n" );
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document.write( " So this is the other answer \n" );
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document.write( " <---------------------------------Other answer \n" );
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document.write( " So our solution is \n" );
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document.write( " and  \n" );
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document.write( " which can also look like \n" );
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document.write( " ( , ) \n" );
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document.write( " Notice if we graph the equations (if you need help with graphing, check out this solver) \n" );
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document.write( " we get \n" );
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document.write( " graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle. \n" );
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document.write( " and we can see that the two equations intersect at ( , ). This verifies our answer. \n" );
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document.write( " Check: \n" );
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document.write( " Plug in ( , ) into the system of equations \n" );
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document.write( " Let and . Now plug those values into the equation  \n" );
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document.write( " Plug in and  \n" );
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document.write( " Multiply \n" );
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document.write( " Add \n" );
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document.write( " Reduce. Since this equation is true the solution works. \n" );
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document.write( " So the solution ( , ) satisfies  \n" );
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document.write( " Let and . Now plug those values into the equation  \n" );
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document.write( " Plug in and  \n" );
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document.write( " Multiply \n" );
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document.write( " Add \n" );
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document.write( " Reduce. Since this equation is true the solution works. \n" );
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document.write( " So the solution ( , ) satisfies  \n" );
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document.write( " Since the solution ( , ) satisfies the system of equations \n" );
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document.write( " this verifies our answer. \n" );
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