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Find an ordered pair (x, y) that solves the system:

 

 \(\begin{align*} 2x - 3y &= -3.2 - 0.2x + 0.1y,\\ x &= 0.6x - y + 8.8 \end{align*}\)

 Jul 15, 2019
 #1
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2x - 3y  = -3.2 - 0.2x  + 0.1y

x = 0.6x - y + 8.8

 

Multiply both equations through by 10 to get rid of the decimals

 

20x - 30y  = -32 - 2x + y

10x = 6x - 10y + 88

 

Rearrange the equations as

 

22x - 31y  =  -32

4x  + 10y  =  88

 

Multiply the first equation by -4    and the second by 22

 

-88x + 124y  = 128

88x  + 220y  = 1936      add these equations

 

344y  =  2064      divide both sides by 344

y  = 6  

 

And using 4x + 10y  = 88   we can find x as

 

4x + 10 (6)  = 88

4x + 60  = 88     subtract 60 from both sides

4x  =  28            divide both sides by 4

x = 7

 

So  (x, y)  =  ( 7, 6)

 

 

cool cool cool

 Jul 15, 2019

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