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You can put this solution on YOUR website!
There's a good reason why you were having difficulty. Let's see if we can find out why. You are
\n" ); document.write( "given the two equations:
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\n" ); document.write( "-3x + 3y = 4 and
\n" ); document.write( "- x + y = 3
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\n" ); document.write( "Suppose we decide to use variable elimination to solve these two equations. Let's multiply the
\n" ); document.write( "bottom equation (both sides and all terms) by 3. When we do that the set of equations becomes:
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\n" ); document.write( "-3x + 3y = 4 and
\n" ); document.write( "-3x + 3y = 9
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\n" ); document.write( "If you subtract these equations, everything on the left side disappears and the right side
\n" ); document.write( "subtraction results in -5. I'll bet that's exactly what you did. You can tell right away
\n" ); document.write( "why this happened, but let's take a different look at it. Let's convert the two equations to the
\n" ); document.write( "slope-intercept form of y = mx + b in which m (the multiplier of x) is the slope and b (the
\n" ); document.write( "constant) is the value on the y-axis where the graph intercepts the y-axis.
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\n" ); document.write( "Let's work on the converting the first equation as follows:
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\n" ); document.write( "-3x + 3y = 4 <=== add 3x to both sides. On the left side this cancels the -3x & you have:
\n" ); document.write( "3y = 3x + 4 <=== divide both sides (all terms) by 3 to get:
\n" ); document.write( "y = x + 4/3 <=== slope intercept form of the first equation.
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\n" ); document.write( "Next let's work on converting the second equation as follows:
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\n" ); document.write( "-3x + 3y = 9 <=== add 3x to both sides. On the left side this cancels the -3x & you have:
\n" ); document.write( "3y = 3x + 9 <=== divide both sides (all terms) by 3 to get:
\n" ); document.write( "y = x + 3 <=== slope intercept form of the second equation.
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\n" ); document.write( "Look at both the slope intercept forms. In both of these equations the multiplier of the
\n" ); document.write( "x is 1. This means that the graphs of each of these equations has a slope of 1. And from
\n" ); document.write( "the constants you can tell that one crosses the x axis at +4/3 and the other crosses at
\n" ); document.write( "x = +3. Since the slopes are equal the graphs are parallel and are separated vertically.
\n" ); document.write( "To have a common solution the graphs must cross, but parallel lines do not cross. This
\n" ); document.write( "means that these two equations do not have a common solution, and that is why you were
\n" ); document.write( "having trouble figuring out what you were doing wrong. You weren't doing anything wrong ...
\n" ); document.write( "you just needed to understand what was going on. And just for grins, here's the graphs of the two
\n" ); document.write( "equations so you can see what I mean. The \"rust red\" graph is for the top equation, and
\n" ); document.write( "the green graph is for the bottom equation:
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\n" ); document.write( "Hope this helps you to understand the problem a little better.
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