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Solve the System for x and y

{12/x + 5/y = 8

{8/x - 3/y = -1

ManuelBautista2019  Dec 6, 2017

#1
+5576
+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
Sort:

#1
+5576
+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

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