Respuesta :
Answer:
The value of x , y for given linear equation using elimination is [tex]\dfrac{- 17}{11}[/tex] , [tex]\dfrac{ 14}{11}[/tex] .
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 = [tex]\dfrac{42}{33}[/tex]
dividing numerator and denominator by 3
i.e y = [tex]\dfrac{14}{11}[/tex]
So, The value of y = [tex]\dfrac{14}{11}[/tex]
Now, Put the value of y into eq C
∵ - 6 x + 21 y = 36
Or, - 6 x + 21 × [tex]\dfrac{14}{11}[/tex] = 36
Or, - 6 x + [tex]\dfrac{294}{11}[/tex] = 36
Or, - 6 x = 36 - [tex]\dfrac{294}{11}[/tex]
Or, - 6 x = [tex]\dfrac{396 - 294}{11}[/tex]
Or, - 6 x = [tex]\dfrac{102}{11}[/tex]
∴ x = [tex]\frac{102}{11\times (-6)}[/tex]
i.e x = [tex]\dfrac{- 17}{11}[/tex]
So, The value of x = [tex]\dfrac{- 17}{11}[/tex]
Hence, The value of x , y for given linear equation using elimination is [tex]\dfrac{- 17}{11}[/tex] , [tex]\dfrac{ 14}{11}[/tex] . Answer
