Question

-2x+7y=12 3x+6y =3 solve by elimination

Answer 1

Answer:

The value of x , y for given linear equation using elimination is   $\dfrac{- 17}{11}$ ,  $\dfrac{ 14}{11}$  .

Step-by-step explanation:

Given as :

The two linear equation are

-2 x + 7 y = 12                   .............A

3 x + 6 y = 3                    .............B

Solving the equation using elimination method

Now, multiply the equation A by 3

i.e 3 × ( - 2 x + 7 y ) = 3 × 12

Or, - 6 x + 21 y = 36                .......C

Again

multiply the equation B by 2

i.e 2 × ( 3 x + 6 y ) = 2 × 3

Or, 6 x + 12 y = 6                .....D

Now, Solving equation C an D

( - 6 x + 21 y ) + ( 6 x + 12 y ) = 36 + 6

Or , ( - 6 x + 6 x ) + ( 21 y + 12 y ) = 42

Or, (0) + (33 y ) = 42

Or, 33 y = 42

∴   y = $\dfrac{42}{33}$

dividing numerator and denominator by 3

i.e y = $\dfrac{14}{11}$

So, The value of y = $\dfrac{14}{11}$

Now, Put the value of y into eq C

∵ - 6 x + 21 y = 36                

Or, - 6 x + 21 × $\dfrac{14}{11}$ = 36        

Or, - 6 x + $\dfrac{294}{11}$ = 36      

Or, - 6 x = 36 -  $\dfrac{294}{11}$

Or, - 6 x =  $\dfrac{396 - 294}{11}$

Or, - 6 x =  $\dfrac{102}{11}$

∴  x = $\frac{102}{11\times (-6)}$

i.e x =  $\dfrac{- 17}{11}$

So, The value of x = $\dfrac{- 17}{11}$

Hence, The value of x , y for given linear equation using elimination is   $\dfrac{- 17}{11}$ ,  $\dfrac{ 14}{11}$  . Answer