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if
(2)/(x + 1) + (8)/(y - 3) = (10)/(3)and
(4)/(x + 1) - (2)/(y - 3) = (2)/(3) what is the value of x + y?

if (2)/(x + 1) + (8)/(y - 3) = (10)/(3)and (4)/(x + 1) - (2)/(y - 3) = (2)/(3) what-example-1

1 Answer

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x\text{ + y = 8}

Here, we want to get the value of x + y

We proceed as follows;

From the second equation, we have that;


(2)/(y-3)\text{ = }(4)/(x+1)-(2)/(3)

We can rewrite the first equation as;


(2)/(x+1)+4((2)/(y-3))\text{ = }(10)/(3)

We substitute the first equation above in the second

Thus, we have that;


\begin{gathered} (2)/(x+1)\text{ + 4(}(4)/(x+1)-(2)/(3))\text{ = }(10)/(3) \\ \\ (2)/(x+1)+(16)/(x+1)-(8)/(3)\text{ = }(10)/(3) \\ \\ (18)/(x+1)\text{ = }(10)/(3)+(8)/(3) \\ \\ (18)/(x+1)\text{ = }(18)/(3) \\ \\ x+1\text{ = 3} \\ x\text{ = 3-1} \\ x\text{ = 2} \end{gathered}

We then proceed to get the value of y by substituting the obtained value of x

We have this as;


\begin{gathered} (2)/(y-3)\text{ =}(4)/(x+1)-(2)/(3) \\ \\ (2)/(y-3)\text{ = }(4)/(3)-(2)/(3) \\ \\ (2)/(y-3)\text{ = }(2)/(3) \\ \\ y-3\text{ = 3} \\ y\text{ = 3+ 3 = 6} \end{gathered}

Thus, we have the value of x + y as;


x\text{ + y = 2 + 6 = 8}

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