Question

8/x+12/y=1/5
6/x+8/y=1/7
solve by elimination method
plz answer in full steps

Answer 1

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$\dfrac{8}{x} + \dfrac{12}{y} = \dfrac{1}{5}$

$\dfrac{6}{x} + \dfrac{8}{y} = \dfrac{1}{7}$

solve by elimination method

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${\underline{\huge{\mathbf{\color{pink}{solution}}}}}$

let $\dfrac{1}{x}$ be a

let $\dfrac{1}{y}$ be b

• putting a and b

$8a + 12b = \dfrac{1}{5}$

$6a + 8b = \dfrac{1}{7}$

$5(8a + 12b) = 1$

$7(6a+8b) = 1$

$40a + 60b = 1$----------(i)

$42a + 56b = 1$----------(ii)

• using elimination method

multiply eq (i) by 21 and eq (ii) by 20

$840a + 1260b = 21$-----------(iii)

$840a + 1120b = 20$-----------(iv)

• subtracting eq (iii) by eq (iv)

$840a + 1260b = 21$

$840a + 1120b = 20$

$-\:\:\:\:\:\:\:-\:\:\:\:\:\:\:-$

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$140b = 1$

$b = \dfrac{1}{140}$

• putting value of b in eq (iii)

$840a + 1260b = 21$

$840a + \dfrac{1260}{140}= 21$

$840a + 9= 21$

$840a = 21-9$

$a = \dfrac{12}{840}$

$a = \dfrac{1}{70}$

• putting value of a and b in x and y

$a = \dfrac{1}{x}$

$\dfrac{1}{70} = \dfrac{1}{x}$

$x = 70$

$b = \dfrac{1}{y}$

$\dfrac{1}{140} = \dfrac{1}{y}$

$y = 140$

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THANK YOU ❤

Answer 2

Answer:

8

+

y

12

=

5

1

\dfrac{6}{x} + \dfrac{8}{y} = \dfrac{1}{7}

x

6

+

y

8

=

7

1

solve by elimination method

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{\underline{\huge{\mathbf{\color{pink}{solution}}}}}

solution

let \dfrac{1}{x}

x

1

be a

let \dfrac{1}{y}

y

1

be b

putting a and b

8a + 12b = \dfrac{1}{5}8a+12b=

5

1

6a + 8b = \dfrac{1}{7}6a+8b=

7

1

5(8a + 12b) = 15(8a+12b)=1

7(6a+8b) = 17(6a+8b)=1

40a + 60b = 140a+60b=1 ----------(i)

42a + 56b = 142a+56b=1 ----------(ii)

using elimination method

multiply eq (i) by 21 and eq (ii) by 20

840a + 1260b = 21840a+1260b=21 -----------(iii)

840a + 1120b = 20840a+1120b=20 -----------(iv)

subtracting eq (iii) by eq (iv)

840a + 1260b = 21840a+1260b=21

840a + 1120b = 20840a+1120b=20

-\:\:\:\:\:\:\:-\:\:\:\:\:\:\:-−−−

_________________________

140b = 1140b=1

b = \dfrac{1}{140}b=

140

1

putting value of b in eq (iii)

840a + 1260b = 21840a+1260b=21

840a + \dfrac{1260}{140}= 21840a+

140

1260

=21

840a + 9= 21840a+9=21

840a = 21-9840a=21−9

a = \dfrac{12}{840}a=

840

12

a = \dfrac{1}{70}a=

70

1

putting value of a and b in x and y

a = \dfrac{1}{x}a=

x

1

\dfrac{1}{70} = \dfrac{1}{x}

70

1

=

x

1

x = 70x=70

b = \dfrac{1}{y}b=

y

1

\dfrac{1}{140} = \dfrac{1}{y}

140

1

=

y

1

y = 140y=140

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THANK YOU ❤