Question

\frac { 2 y + 4 } { 2 y - 6 } = \frac { - 2 } { 5 }2y−62y+4​=5−2​

Answer 1

Answer:

Let  

2x+3y

1

​

=u and  

3x−2y

1

​

=v. Then, the given system of equations becomes

2

1

​

u+  

7

12

​

v=  

2

1

​

⇒7u+24v=7  ..(i)

and, 7u+4v=2 .(ii)

Substracting equation (ii) from equation (i), we get

20v=5⇒v=  

4

1

​

 

Putting v=  

4

1

​

 in equation (i), we get

7u+6=7⇒u=  

7

1

​

 

Now, u=  

7

1

​

⇒  

2x+3y

1

​

=  

7

1

​

⇒2x+3y=7 (iii)

and, u=  

4

1

​

⇒  

3x−2y

1

​

=  

4

1

​

⇒3x−2y=4 .(iv)

Multiplying equation (iii) by 2 and equation (iv) by 3, we get

4x+6y=14  .(v)

9x−6y=12 .(vi)

Adding equations (v) and (vi), we get

13x=26⇒x=2

Putting x=2 in equation(v), we get

8+6y=14⇒y=1

Hence, x=2,y=1 is the solution of the given system of equations.

Step-by-step explanation:

Answer 2

Answer:

$\bf \implies\frac { 2 y + 4 } { 2 y - 6 } = \frac { - 2 } { 5 }$

$\bf \implies \: cross \: multification \: we \: get$

$\bf \implies(2y + 4)5 = (2y - 6)( - 2)$

$\bf \implies10y+20=\left(2y-6\right)\left(-2\right)$

$\bf \implies10y+20=-4y+12$

$\bf \implies10y + 4y = 12 - 20$

$\bf \implies14y = - 8$

$\bf \implies \: y = - \frac{8}{14}$

$\boxed{\pink{ \bf \implies \: y = - \frac{4}{7}}}$

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