Question

2x+x-y/6=2,x-2x+y/3=1 solve by simultaneous linear equation with elimination method

Answer 1

GIVEN :

$2x+(\frac{x-y}{6})=2$ , $x-(\frac{2x+y}{3})=1$  solve by simultaneous linear equations with elimination method

TO FIND :

The values of x and y and solution to the given simultaneous linear equations with elimination method

SOLUTION :

Given that the simultaneous linear equations are $2x+(\frac{x-y}{6})=2$ , $x-(\frac{2x+y}{3})=1$

Now solving the given equations $2x+(\frac{x-y}{6})=2$ , $x-(\frac{2x+y}{3})=1$

$2x+(\frac{x-y}{6})=2$

$\frac{12x+x-y}{6}=2$

$13x-y=12\hfill (1)$

and  $x-(\frac{2x+y}{3})=1$

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

$x-y=3\hfill (2)$

Now solving the equations (1) and (2) by using the Elimination method :

Subtracting the equations (1) and (2)

13x-y=12

x - y = 3

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

12x+0=9

$x=\frac{9}{12}$

$x=\frac{3}{4}$

Substitute the value $x=\frac{3}{4}$ in the equation (2) we get

$\frac{3}{4}-y=3$

$-y=3-\frac{3}{4}$

$-y=\frac{12-3}{4}$

$y=-\frac{9}{4}$

∴ the values are  $x=\frac{3}{4}$ and $y=-\frac{9}{4}$

∴  solution to the given simultaneous linear equation by using Elimination method is $(\frac{3}{4},-\frac{9}{4})$.

Answer 2

Answer:

2x+(

6

x−y

)=2 , x-(\frac{2x+y}{3})=1x−(

3

2x+y

)=1 solve by simultaneous linear equations with elimination method

TO FIND :

The values of x and y and solution to the given simultaneous linear equations with elimination method

SOLUTION :

Given that the simultaneous linear equations are 2x+(\frac{x-y}{6})=22x+(

6

x−y

)=2 , x-(\frac{2x+y}{3})=1x−(

3

2x+y

)=1

Now solving the given equations 2x+(\frac{x-y}{6})=22x+(

6

x−y

)=2 , x-(\frac{2x+y}{3})=1x−(

3

2x+y

)=1

2x+(\frac{x-y}{6})=22x+(

6

x−y

)=2

\frac{12x+x-y}{6}=2

6

12x+x−y

=2

13x-y=12\hfill (1)13x−y=12\hfill(1)

and x-(\frac{2x+y}{3})=1x−(

3

2x+y

)=1

\frac{3x-2x-y}{3}=1

3

3x−2x−y

=1

x-y=3\hfill (2)x−y=3\hfill(2)

Now solving the equations (1) and (2) by using the Elimination method :

Subtracting the equations (1) and (2)

13x-y=12

x - y = 3

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

12x+0=9

x=\frac{9}{12}x=

12

9

x=\frac{3}{4}x=

4

3

Substitute the value x=\frac{3}{4}x=

4

3

in the equation (2) we get

\frac{3}{4}-y=3

4

3

−y=3

-y=3-\frac{3}{4}−y=3−

4

3

-y=\frac{12-3}{4}−y=

4

12−3

y=-\frac{9}{4}y=−

4

9

∴ the values are x=\frac{3}{4}x=

4

3

and y=-\frac{9}{4}y=−

4

9

∴ solution to the given simultaneous linear equation by using Elimination method is (\frac{3}{4},-\frac{9}{4})(

4

3

,−

4

9

)