Question

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

Answer 1

The value of x , y for given linear equation using elimination is
`(- 17)/(11)` ,
`( 14)/(11)` .

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 =
`(42)/(33)`

dividing numerator and denominator by 3

i.e y =
`(14)/(11)`

So, The value of y =
`(14)/(11)`

Now, Put the value of y into eq C

∵ - 6 x + 21 y = 36

Or, - 6 x + 21 ×
`(14)/(11)` = 36

Or, - 6 x +
`(294)/(11)` = 36

Or, - 6 x = 36 -
`(294)/(11)`

Or, - 6 x =
`(396 - 294)/(11)`

Or, - 6 x =
`(102)/(11)`

∴ x =
`(102)/(11* (-6))`

i.e x =
`(- 17)/(11)`

So, The value of x =
`(- 17)/(11)`

Hence, The value of x , y for given linear equation using elimination is
`(- 17)/(11)` ,
`( 14)/(11)` . Answer