Question

The solution of 2x-5y=4 and 3x-2y=12 is​

Answer 1

Answer:

Value of x is 52 / 11 and the value of your is 12 / 11.

Step-by-step explanation:

Given,

2x - 5y = 4 ... ( 1 )

3x - 2y = 12 ... ( 2 )

Multiplying the right hand side as well as the left hand side of ( 1 ) by 3 & multiplying the right hand side as well as the left hand side of ( 2 ) by 2.

3 × [ 2x - 5y ] = 3 × 4 { ( 1 ) multiplied by 3 }

= > 6x - 15y = 12 ...( 3 )

2 x [ 3x - 2y ] = 2 × 12 { ( 2 ) multiplied by 2 }

= > 6x - 4y = 24 ...( 4 )

Subtracting ( 4 ) from ( 3 ) :

= > ( 6x - 15y ) - ( 6x - 4y ) = 12 - 24

= > 6x - 15y - 6x + 4y = - 12

= > - 15y + 4y = - 12

= > - 11y = - 12

= > y = 12 / 11

Substituting the value of y in ( 1 ) :

= > 2x - 5( 12 / 11 ) = 4

= > 2x - ( 60 / 11 ) = 4

= > x - ( 30 / 11 ) = 2 { cancelling 2 from both sides, as it's common }

= > x = 2 + ( 30 / 11 )

= > x = ( 22 + 30 ) / 11

= > x = 52 / 11

Required value of x is 52 / 11 and the value of your is 12 / 11.

Answer 2

Answer:

$\large\bold\red{x = \frac{52}{11} }\\\\\large\bold\red{y = \frac{12}{11} }$

Step-by-step explanation:

Given,

Linear Equations,

$2x - 5y = 4 \: \: \: \: .........(1) \\ \\ 3x - 2y = 12 \: \: \: \: ........(2)$

Now,

From Equation (1) ,

We get,

$= > 5y = 2x - 4 \\ \\ = > y = \frac{2x - 4}{5}$

Further,

Substituting the value of 'y' in Equation (2),

We get,

$= > 3x - 2( \frac{2x - 4}{5} ) = 12 \\ \\ = > 3 x - \frac{4x - 8}{5} = 12 \\ \\ = > \frac{15x - (4x - 8)}{5} = 12 \\ \\ = > 15x - 4x + 8 = 12 \times 5 \\ \\ = > 11x + 8 = 60 \\ \\ = > 11x = 60 - 8 \\ \\ = > \large \boxed{ \bold{x = \frac{52}{11} }}$

Putting this value,

We get,

$= > y = \frac{2( \frac{52}{11} ) - 4}{5} \\ \\ = > y = \frac{104 - 44}{11 \times 5} \\ \\ = > y = \frac{60}{55} \\ \\ = > \large \boxed{ \bold{y = \frac{12}{11} }}$