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Help me Please

Solve the System for x and y

 

{12/x + 5/y = 8

{8/x - 3/y = -1

ManuelBautista2019  Dec 6, 2017

Best Answer 

 #1
avatar+7324 
+1

\(\frac{12}{x}+\frac5y=8\\ \frac8x-\frac3y=-1 \)

                                           This is the same as....

\(12(\frac1x)+5(\frac1y)=8 \\ 8(\frac1x)-3(\frac1y)=-1\)

                                           Multiply the top equation through by  2 , and

                                           multiply the bottom equation through by  -3 .

\(24(\frac1x)+10(\frac1y)=16 \\ -24(\frac1x)+9(\frac1y)=3 \)

                                           Add the two equations together and solve for  y .

\(19(\frac1y)=19 \\ 19=19y\\ \color{Emerald}1=y\)

                            Plug in  1  for  y  in one of the original equations to find  x .

\(\frac{12}{x}+\frac51=8 \\ \frac{12}x=3 \\ 12=3x\\ \color{Emerald}4=x\)

hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017
 #1
avatar+7324 
+1
Best Answer

\(\frac{12}{x}+\frac5y=8\\ \frac8x-\frac3y=-1 \)

                                           This is the same as....

\(12(\frac1x)+5(\frac1y)=8 \\ 8(\frac1x)-3(\frac1y)=-1\)

                                           Multiply the top equation through by  2 , and

                                           multiply the bottom equation through by  -3 .

\(24(\frac1x)+10(\frac1y)=16 \\ -24(\frac1x)+9(\frac1y)=3 \)

                                           Add the two equations together and solve for  y .

\(19(\frac1y)=19 \\ 19=19y\\ \color{Emerald}1=y\)

                            Plug in  1  for  y  in one of the original equations to find  x .

\(\frac{12}{x}+\frac51=8 \\ \frac{12}x=3 \\ 12=3x\\ \color{Emerald}4=x\)

hectictar  Dec 6, 2017
edited by hectictar  Dec 6, 2017

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