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You can put this solution on YOUR website!
y = 3x + 2 and y = 3x - 4 ... solve by graphing
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\n" ); document.write( "I'm beginning to play with the graphing system provided by this site, so bear with me.
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\n" ); document.write( "The two equations are in the slope intercept form. This form is
\n" ); document.write( "letter m represents the slope of the line and the letter b represents where the line
\n" ); document.write( "crosses the y-axis.
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\n" ); document.write( "Notice that in each of these equations the slope (the number that multiplies the x term)
\n" ); document.write( "is +3. That means the two equations slope up as you move to the right, and the slope of
\n" ); document.write( "+3 means that for every unit you move to the right, the graph goes up +3 units.
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\n" ); document.write( "Think about that. The graphs for these two equations are parallel lines! Therefore,
\n" ); document.write( "they never cross. The only difference is that the first line crosses the y-axis at +2,
\n" ); document.write( "and the second line crosses the y-axis at -4.
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\n" ); document.write( "Let's show this on a graph:
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\n" ); document.write( "I just looked at the graph I drew. Sort of cool! The red line is the graph of the
\n" ); document.write( "first equation
\n" ); document.write( "plus 3. Pick a point on the graph. Then move from that point horizontally to the right 1 unit.
\n" ); document.write( "From that point you should have to move up 3 units to get back on the graph. That shows
\n" ); document.write( "that the graph has a slope of +3. Notice also that b in the equation was +2 and we said
\n" ); document.write( "that b was the point of intercept on the y-axis. And from the above graph you can see
\n" ); document.write( "that the red line does cross the y-axis at +2. The green line represents the second
\n" ); document.write( "equation
\n" ); document.write( "that its slope is also 3 (which is the multiplier of the x term in the equation) and that
\n" ); document.write( "the b value from the equation equals the point where the graph crosses the y-axis.
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\n" ); document.write( "But the important thing to note is that the two lines are parallel. They never cross.
\n" ); document.write( "But a system of two linear equations such as these has three possibilities: (1) every
\n" ); document.write( "solution of one equation is also a solution of the other. In this case the two graphs
\n" ); document.write( "lie one on top of the other. (2) there is 1 common solution, that is one point where the
\n" ); document.write( "values for x and y will satisfy both equations. If this is the case, the two graphs
\n" ); document.write( "will cross at that point. and (3) there is no common solution because the graphs do not lie
\n" ); document.write( "on top of each other, and the two graphs do not cross at any point.
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\n" ); document.write( "In the problem number (3) above applies. The graphs are parallel and by definition
\n" ); document.write( "parallel lines never meet or intersect. Also the graphs obviously do not lie on top of
\n" ); document.write( "each other. They are always separated by 6 units (look at the distance between the lines
\n" ); document.write( "on the y-axis. From -4 to + 2 is 6 units of separation, and that vertical separation
\n" ); document.write( "remains unchanged at any point.
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\n" ); document.write( "How about that. A trick question about finding the common solution. I hope this helps
\n" ); document.write( "with your understanding of graphically solving a system of two linear equations. \n" ); document.write( "