Question

solve by elimination 1 upon 2 bracket open x + 2 Y bracket close + 5 upon 3 bracket open x 3 x - 2 Y bracket close is equals to minus 3 upon 2,5 upon 4 bracket open x + 2 Y bracket close minus 3 upon X bracket open 3 X - 2 Y bracket close is equals to 61 upon 60​

Answer 1

GIVEN :

The equations are $\frac{1}{2(x+2y)}+\frac{5}{3(3x-2y)}=-\frac{3}{2}$ and $\frac{5}{4(x+2y)}-\frac{3}{5(3x-2y)}=\frac{61}{60}$

TO FIND :

The values of x and y in the given equations by using the Elimination method.

SOLUTION :

Given that the equations are

$\frac{1}{2(x+2y)}+\frac{5}{3(3x-2y)}=-\frac{3}{2}\hfill (1)$ and $\frac{5}{4(x+2y)}-\frac{3}{5(3x-2y)}=\frac{61}{60}\hfill (2)$

Solving the given equations by using the Elimination method.

Let $\frac{1}{x+2y}=u$ and $\frac{1}{3x-2y}=v$

Now the equations (1) and (2) becomes,

$\frac{u}{2}+\frac{5v}{3}=-\frac{3}{2}\hfill (3)$

and $\frac{5u}{4}-\frac{3v}{5}=\frac{61}{60}\hfill (4)$

From equation (4)

$\frac{5u}{4}=\frac{61}{60}+\frac{3v}{5}$

$u=(\frac{61}{60}+\frac{3v}{5})\frac{4}{5}$

$u=\frac{61}{75}+\frac{12v}{25}\hfill (A)$

Substitute the value of u in the equation (3) we get,

$\frac{1}{2}(\frac{61}{75}+\frac{12v}{25})+\frac{5v}{3}=-\frac{3}{2}$

$\frac{61}{150}+\frac{6v}{25}+\frac{5v}{3}=-\frac{3}{2}$

$\frac{18v+125v}{75}=-\frac{3}{2}-\frac{61}{150}$

$\frac{143v}{75}=\frac{-225-61}{150}$

$143v=-\frac{286}{2}$

$v=-\frac{143}{143}$

∴ v=-1

Substitute the value of v in the equation (A) we get,

$u=\frac{61}{75}+\frac{12}{25}(-1)$

$u=\frac{61}{75}-\frac{12}{25}$

$u=\frac{61-36}{75}$

$u=\frac{25}{75}$

∴ $u=\frac{1}{3}$

From equations $\frac{1}{x+2y}=u$ and $\frac{1}{3x-2y}=v$ we can substitute the values of u and v we have that,

$\frac{1}{x+2y}=\frac{1}{3}$ and $\frac{1}{3x-2y}=-1$

$x+2y=3\hfill (5)$ and 1=-1(3x-2y) ⇒$-3x+2y=1\hfill (6)$

Now subtracting the equations (5) and (6)

x+2y=3

-3x+2y=1

(+)_(-)__(-)___

4x=4

$x=\frac{4}{4}$

∴ x=1            

Substituting the value of x in the equation (5),

1+2y=3

2y=3-1

2y=2

$y=\frac{2}{2}$

∴ y=1    

∴the values are  x=1 and y=1          

Answer 2

Answer:

Same as given in the first answer