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document.write( " Lets start with the given system of linear equations
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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.
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document.write( " Solve for y for the first equation
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document.write( "  Subtract  from both sides
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document.write( "  Divide both sides by -1.
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document.write( " Which breaks down and reduces to
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document.write( "  Now we've fully isolated y
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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.
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document.write( "  Replace y with . Since this eliminates y, we can now solve for x.
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document.write( "  Distribute -1 to
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document.write( "  Multiply
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document.write( " Reduce any fractions
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document.write( "  Subtract  from both sides
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document.write( "  Combine the terms on the right side
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document.write( "  Now combine the terms on the left side.
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document.write( "  Since this expression is not true, we have an inconsistency.
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document.write( " So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.
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document.write( "  graph of (red) and (green) (hint: you may have to solve for y to graph these)
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document.write( " and we can see that the two equations are parallel and will never intersect. So this system is inconsistent |
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