SOLUTION: y=3x+2 Y=3x-4 solve system by graphing

Question 72028: y=3x+2 Y=3x-4 solve system by graphing
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
y = 3x + 2 and y = 3x - 4 ... solve by graphing
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I'm beginning to play with the graphing system provided by this site, so bear with me.
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The two equations are in the slope intercept form. This form is where the
letter m represents the slope of the line and the letter b represents where the line
crosses the y-axis.
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Notice that in each of these equations the slope (the number that multiplies the x term)
is +3. That means the two equations slope up as you move to the right, and the slope of
+3 means that for every unit you move to the right, the graph goes up +3 units.
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Think about that. The graphs for these two equations are parallel lines! Therefore,
they never cross. The only difference is that the first line crosses the y-axis at +2,
and the second line crosses the y-axis at -4.
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Let's show this on a graph:
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I just looked at the graph I drew. Sort of cool! The red line is the graph of the
first equation . See if you can verify that the slope of this line is
plus 3. Pick a point on the graph. Then move from that point horizontally to the right 1 unit.
From that point you should have to move up 3 units to get back on the graph. That shows
that the graph has a slope of +3. Notice also that b in the equation was +2 and we said
that b was the point of intercept on the y-axis. And from the above graph you can see
that the red line does cross the y-axis at +2. The green line represents the second
equation . You can do the same analysis process to prove to yourself
that its slope is also 3 (which is the multiplier of the x term in the equation) and that
the b value from the equation equals the point where the graph crosses the y-axis.
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But the important thing to note is that the two lines are parallel. They never cross.
But a system of two linear equations such as these has three possibilities: (1) every
solution of one equation is also a solution of the other. In this case the two graphs
lie one on top of the other. (2) there is 1 common solution, that is one point where the
values for x and y will satisfy both equations. If this is the case, the two graphs
will cross at that point. and (3) there is no common solution because the graphs do not lie
on top of each other, and the two graphs do not cross at any point.
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In the problem number (3) above applies. The graphs are parallel and by definition
parallel lines never meet or intersect. Also the graphs obviously do not lie on top of
each other. They are always separated by 6 units (look at the distance between the lines
on the y-axis. From -4 to + 2 is 6 units of separation, and that vertical separation
remains unchanged at any point.
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How about that. A trick question about finding the common solution. I hope this helps
with your understanding of graphically solving a system of two linear equations.
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