Two symbolic techniques
used to solve linear equations are; graphically, and algebraically. Personally
I prefer to use graphically the most because it is the fastest method to solve
the equation, also it is easy to solve with a calculator.
To solve an equation
graphically you must first set it into slope intercept form. This is achieved
by setting the equation equal to Y. In this given problem, x + y = 10,
and 3x+2y=20 we will solve for y. You get -x+10
= y and -3/2x+10=y. When graphing these two numbers check to see where they
intersect, which is at (0,10). Where they intercept is the answer to the
problem.
The second method to solve by is algebraically. This method uses
substitution and can be a bit confusing if a clear paper trail is not kept when
doing your homework. Given the same problem, x+y=10, and 3x+2y=20 we will take the
first half of the problem and set it all equal to y. We get –x+10=y. Given this
information, take the y value and substitute it into the other problem (3x+2y=20).
Substituted we get, (3x-2x+20=20) Simplified the equation comes out to
(x+20=20). Therefore the value of x is 0. We then take this value of x and
substitute it into the first half of the
WHAT AN EXTREMELY LONG DQ ANSWER!
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linear equation. Where (x+y=10) when substituted this turns into (0+y=10) Therefore the value of Y is 10. Given this information we can conclude that the answer to this linear equation is (0,10) (x,y).
WHAT AN EXTREMELY LONG DQ ANSWER!
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linear equation. Where (x+y=10) when substituted this turns into (0+y=10) Therefore the value of Y is 10. Given this information we can conclude that the answer to this linear equation is (0,10) (x,y).
A third valuable method is to solve by elimination. Given the same
problem, x+y=10, and 3x+2y=20, we will solve by eliminating the variable x.
The goal here is to make it so that the x values will cancel out when the
problem is combined together. The first step is to multiply the first linear
equation by -3. This is done here -3(x+y=10) we get, -3x-3y=-30. This new
linear equation is combined with the second one, (3x+2y=20). Together when
combined This new equation comes out to (3x-3x+2y-3y=-10) When canceled out it
becomes, -y=-10. y therefore equals 10. We plug this value back into either one
of the original linear equations, and can conclude that x is again 0.
In conclusion I feel that the first method, solving graphically, is a
far faster method to solve the problem. Not only that, but you can see just by
the explanation of the two types that substituting and solving algebraically
takes longer to explain, and longer to follow through with.
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ReplyDeleteYou read my mind, took the words right out of my mouth, whatever you wanna call it. I notice the SAME thing! Not too smart on their behalf..
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