Question

x-2y/3=8/3 2x/5-y=7/5 by elimination ​

Answer 1

Answer:

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Step-by-step explanation:

Pls refer to the attachment

Answer 2

Answer:-

The value of x and y are $\bf\dfrac{26}{11}\:\:And\:\:-\dfrac{5}{11}.$ respectively.

Explanation:-

Given Equations:-

$\\ \bf\longrightarrow x - \dfrac{2y}{3} = \dfrac{8}{3}....(1)$

$\\ \bf\longrightarrow\dfrac{2x}{5} - y= \dfrac{7}{5}....(1)$

To Find:-

• The value of x and y by elimination method.

Now,

By simplifying eq(1),

$\\ \tt\mapsto x - \frac{2y}{3} = \frac{8}{3} .$

$\\ \tt\mapsto \frac{3x - 2y}{ \cancel3} = \frac{8}{ \cancel3} . \\ \\ \rm(taking \: \: lcm).$

$\\ \mapsto \boxed{ \bf 3x - 2y = 8....(3)}.$

Again by simplifying eq(2),

$\\ \tt\mapsto \frac{2x}{5} - y = \frac{7}{5} .$

$\\ \tt\mapsto \frac{2x - 5y}{\cancel5} = \frac{7}{ \cancel5} .$

$\\ \mapsto \boxed{ \bf 2x - 5y = 7....(4)}.$

Now,

By Multiplying eq(3) by 2 we get,

$\\ \tt\mapsto2 \times \bigg(3x - 2y = 8 \bigg).$

$\\ \mapsto \boxed{ \bf 6x - 4y = 16....(5)}.$

Again By Multiplying eq(4) by 3 we get,

$\\ \tt\mapsto3 \times \bigg(2x - 5y = 7 \bigg).$

$\\ \mapsto \boxed{ \bf6x - 15y = 21...(6)}.$

So,

By subtracting eq(5) from eq(6) we get,

$\\ \tt\mapsto \bigg(6x - 15y \bigg) - \bigg(6x - 4y \bigg) = 21 - 16.$

$\\ \tt\mapsto \cancel{6x} \: - 15y \: \cancel{ - 6x} \: + 4y = 5.$

$\\ \tt\mapsto - 11y = 5.$

$\\ \mapsto \boxed{ \bf y = - \frac{ 11}{5} }.$

By Putting The Value of y in eq(5) we get,

$\\ \tt\mapsto6x - 4y = 16.$

$\\ \tt\mapsto6x - 4 \bigg( - \frac{5}{11} \bigg) = 16.$

$\\ \tt\mapsto6x + \frac{20}{11} = 16.$

$\\ \tt\mapsto \frac{66x + 20}{11} = 16.$

$\\ \tt\mapsto66x + 20 = 16 \times 11.$

$\\ \tt\mapsto66 x + 20 = 176.$

$\\ \tt\mapsto66x = 156.$

$\\ \tt\mapsto x = \frac{156}{66} .$

$\\ \mapsto \boxed{ \bf x = \frac{26}{11} }.$

Therefore the required values of x and y are $\bf\dfrac{26}{11}\:\:And\:\:-\dfrac{5}{11}.$ respectively.