Math, asked by GamesTime990, 3 days ago

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Answered by samdrishtff90
2

Answer:

x = -1/2 and y= 1/2

Step-by-step explanation:

7/x + 8/y = 2 and 2/x + 13/y = 22

let 1/x = m and 1/y = n

then

7m + 8n = 2 and 2m + 13n = 22

multiply equation (1) by 2 and equation (2) by 7

14m+16n=4 and 14m+91n = 154

subtract them

14m-14m+16n-91n = 4-154

-75n = -150

n = 2

7m + 8(2) = 2

7m +16 = 2

7m = 2-16

7m= -14

m=-2

1/x = m

1/x = -2

x = -1/2

1/y =n

1/y = 2

y = 1/2

Answered by Anonymous
36

 \footnotesize \text \blue{Solution:-}

 \:

 \footnotesize \text \red{7/x + 8/y = 2 and 2/x + 13/y = 22}

 \:

 \footnotesize \text \blue{Let 1/x = u and 1/y = v}

 \:

 \footnotesize \text \red{7u + 8v = 2  \:  -  -  -  - equation(1)}

 \footnotesize \text \red{2u + 13v = 22  -  -  -  -  equation(2)}

 \:

 \footnotesize \text \blue{Multiply equation(1) by 2}

 \:

 \footnotesize \text \red{2(7u + 8v = 2)}

 \footnotesize \text \red{14u + 16v = 4  -  -  -  - equation(3)}

 \:

 \footnotesize \text \blue{Multiply equation(2) by 7}

 \:

 \footnotesize \text \red{7(2u + 13v = 22)}

 \footnotesize \text \red{ 14u + 91v = 154  -  -  -  -  equation(4)</p><p>}

 \:

 \footnotesize \text \blue{Use Elimination method to solve equation(3) and (4)</p><p>}

 \:

 \footnotesize \text \red{ 14u + 16v = 4</p><p>}

 \footnotesize \text \red{ 14u + 91v = 154}

 \footnotesize \text \blue{ -  \:  \:  \:  \:  \:  \:   \:   \:  \:   - \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \:  \: - }

 \footnotesize \text \red{ -75v = 150}

 \footnotesize \text \red{ v = -150/-75}

\footnotesize \red \bigstar \footnotesize \text \blue{ v = 2}

 \:

 \footnotesize \text \blue{ Substitute the value of v in equation(1)}

 \:

 \footnotesize \text \red{ 14u + 16 × 2 = 4}

 \footnotesize \text \red{14u + 32 = 4}

 \footnotesize \text \red{14u = 4 - 32}

 \footnotesize \text \red{14u = -28}

 \footnotesize \text \red{u = -28/14}

\footnotesize \red \bigstar \footnotesize \text \blue{ u = -2}

 \:

 \footnotesize \text \red{1/x = u}

 \footnotesize \text \red{1/x = -2}

 \footnotesize \red \bigstar\footnotesize \text \blue{ \: x = -1/2}

 \:

 \footnotesize \text \red{1/y = v}

 \footnotesize \text \red{1/y = 2}

 \footnotesize \red \bigstar\footnotesize \text \blue{ \: y = 1/2}

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