Linear Systems of Equations Question(10 POINTS FOR BEST ANSWER NO JOKE!!!!)?

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PLEASE ANSWER THE LAST TWO QUESTIONS AND EXPLAIN YOURSELF

Here is the system:
x+ 2y = 4

5x - y = 1/5

Examine the constants in both equations and describe any patterns.

Re-write the above two equation in the form y = ax+ b. How are the constants a and b related?

Using technology, create a family of linear equations similar to the example shown above. On the same set of axes, display your equations. Ensure that the family of equations includes several lines with a wide range of gradients.

Closely examine the resulting graphical display. Clearly describe any apparent graphical patterns.

Set up and solve a general 2 X 2 system that incorporates the patterns found above.

Using your solution to the general system, or otherwise, provide a proof of the graphical pattern observed above.





10 POINTS FOR BEST ANSWER!!!
 
x+ 2y = 4
5x - y = 1/5
I suggest you start out with the equation 5x-y=1/5 because it is already mostly solved.
Subtract 5x on both sides.
-y=1/5-5x
Divide by -1 on each side.
y=-1/5+5x
Now plug in what y equals into the first equation to find the value of x.
x+ 2y = 4
x+2(-1/5+5x)=4
Distribute the 2 to the (-1/5+5x) in parentheses by multiplying.
x-2/5+10x=4
Combine like terms.
11x-2/5=4
Add 2/5 to both sides.
11x=4.4
Divide by 11 on each side.
x=2/5 or .4
Now plug in what x equals or 2/5 into what y equals to find the exact value of y.
y=-1/5+5x
y=-1/5+5(2/5)
y=-1/5+2
y=9/5 or 1.8
Your final answers for (x,y) are (2/5,9/5). To check your work, plug in 2/5 for x and 9/5 for y in one of the Original equations. If you come up with a true statement, then you know your answer has to be correct.
PROOF:
x+ 2y = 4
2/5+2(9/5)=4
2/5+3.6=4
4=4
Because this is a TRUE statement, you can be certain that you have the correct values for x and y.
Hope I helped!
Maxwell
 
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