Question

solve the following linear equation in two variables- [(2/3x+2y)+(3/3x-2y)= 17/5], [(5/3x+2y)+(1/3x-2y)=2]​

Answer 1

Hey friend!

Here is your answer:

Question: Solve the following linear equation in two variables- [(2/3x + 2y) +(3/3x - 2y) = 17/5], [(5/3x + 2y) + (1/3x - 2y) =2]​

Let ¹/(3x + 2y)  be u

and ¹/(3x - 2y) be v

Then,

The new equations are :

2u + 3v = ¹⁷/₅        _eq1

and 5u + v = 2      _eq2

Multiplying eq1  by 1 and eq2 by 3, and subracting them,

we get:

2u + 3v = ¹⁷/₅

15u + 3v = 6

( - )   ( - )   ( - )

-13u = - ¹³/₅

⇒ u = ¹/₅

Putting the value of u in eq 1, we get:

²/₅ + 3v = ¹⁷/₅

⇒ 2 + 15v = 17

⇒ 15v = 17 - 2

⇒ 15v = 15

⇒ v = 1

Now,

¹/(3x + 2y)  = u

⇒ 3x + 2y = 5  _eq3

Also,

¹/(3x - 2y) = v

⇒ 3x - 2y = 1   _eq4

Now, new set of equations are :

3x + 2y = 5  _eq3

and 3x - 2y = 1   _eq4

Subracting eq4 from eq13we get:

4y = 4

⇒ y = 1

Also,

3x - 2 = 1

⇒ 3x = 3

⇒ x = 1

∴ x = 1, y = 1

I hope you understand my solution and if you appreciate my hard work, please respond with a thanks.

Answer 2

Answer:

y = - 1/5

And, x = 5/9

Step-by-step explanation:

Sorry for not giving step by step explanation, if you want it then message me.