Step-by-step EXPLANATION:

Step-by-step explanation:

Given,

Two linear equations such that,

x - \frac{2}{3} y = \frac{8}{3} \: \: .............(1)x−

3

2

y=

3

8

.............(1)

And,

\frac{2}{5} x - y = \frac{7}{5} \: \: \: \: ..........(2)

5

2

x−y=

5

7

..........(2)

Now,

To solve this pair of linear equations,

MULTIPLY the eqn (1) by \frac{2}{5}

5

2

Therefore,

We get,

= > \frac{2}{5} x - \frac{4}{15} y = \frac{16}{15} \: \: \: \: \: ........(3)=>

5

2

x−

15

4

y=

15

16

........(3)

Now,

ELIMINATING the x TERM,

SUBTRACT eqn (3) from eqn (2)

Therefore,

We get,

\begin{lgathered}= > - y - ( - \frac{4}{15} y) = \frac{7}{5} - \frac{16}{15} \\ \\ = > - y + \frac{4}{15} y = \frac{(7 \times 3) - 16}{15} \\ \\ = > \frac{ - 15y + 4y}{ \cancel{15}} = \frac{21 - 16}{ \cancel{15}} \\ \\ = > - 15y + 4y = 21 - 16 \\ \\ = > - 11y = 5 \\ \\ = > \large \boxed{ \bold{y = - \frac{5}{11} }}\end{lgathered}

=>−y−(−

15

4

y)=

5

7

−

15

16

=>−y+

15

4

y=

15

(7×3)−16

=>

15

−15y+4y

=

15

21−16

=>−15y+4y=21−16

=>−11y=5

=>

y=−

11

5

Now,

Putting this value in eqn (2),

We get,

\begin{lgathered}= > x - \frac{2}{3} \times ( - \frac{ 5}{11} ) = \frac{8}{3} \\ \\ = > x + \frac{10}{33} = \frac{8}{3} \\ \\ = > x = \frac{8}{3} - \frac{10}{33} \\ \\ = > x = \frac{(8 \times 11) - 10}{33} \\ \\ = > x = \frac{88 - 10}{33} \\ \\ = > \large \boxed{ \bold{x = \frac{78}{33}}}\end{lgathered}

=>x−

3

2

×(−

11

5

)=

3

8

=>x+

33

10

=

3

8

=>x=

3

8

−

33

10

=>x=

33

(8×11)−10

=>x=

33

88−10

=>

x=

33

78