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Solve the following systems by graphing on your calculator or a website and give the solution. Then show how the solutions would be verified, by using the LEFT SIDE = RIGHT SIDE method. 

 

 

y=2x2+7x−5

y=−1/3x2−2x+9

 Apr 13, 2021
 #1
avatar+493 
+3

Well if ur solving for x, then 2x+ 7x - 5 = -1/3x− 2x + 9

\(2x^3+7x-5=-\frac{1}{3}x^2-2x+9\)

\(=6x^3+21x-15=-x^2-6x+27\)

\(=6x^3+21x-42=-x^2-6x\)

\(=6x^3+27x-42=-x^2\)

\(=6x^3+x^2+27x-42=0\)

\(=x\approx \:1.15942\dots \)

 Apr 13, 2021
 #2
avatar+121004 
+1

See here  : https://www.desmos.com/calculator/oe0gaxs2tt

 

The  solutions  are    ( ≈ -5.046, ≈ 10.604)  and  ( ≈ 1.189, ≈ 6.151)

 

2x^2  + 7x  -  5  =  (-1/3)x^2  - 2x  + 9                   multiply through  by  3

 

6x^2  + 21x  - 15  =  -x^2  - 6x  +  27              rearrange  as

 

7x^2  +  27x - 42  =  0

 

 

Use  the  quad  formula  to get

 

 

x =       -27 ±   sqrt   [ 27^2  -  4 (7) ( -42) ]

          ______________________________

                            2  *  7

 

If  you  calculate  this  correctly  you  should get  the  solutions for   x   shown by  the  graph.....

 

cool cool cool

 Apr 13, 2021

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