Question

5x+3y= -11 , 2x+4y= -10

Answer 1

Given

➝5x + 3y = - 11 (i)

➝2x + 4y = - 10 (ii)

Method - 1 ( Elimination)

➝5x + 3y = - 11 (i) × 2

➝2x + 4y = - 10 (ii) × 5

Now we get

➝10x + 6y = -22 (i)

➝10x + 20y = -50 (ii)

Now Subtracte (ii) from (i)

➝10x + 6y -(10x + 20y )= -22 - ( - 50 )

➝10x + 6y - 10x - 20y = -22 + 50

➝-14y = 28

➝y = -28/14

➝y = -2

Now put the value of y in (i)eq

➝5x + 3y = - 11

➝5x + 3(-2) = -11

➝5x - 6 = -11

➝5x = - 11 + 6

➝5x = -5

➝x = -1

So we get x = -1 and y = -2

Method :- 2 ( Substitution Method)

➝5x + 3y = - 11 (i)

➝2x + 4y = - 10 (ii)

Now take (ii)eq

➝2x + 4y = -10

➝2( x + 2y ) = - 10

➝x + 2y = -5

➝x = -( 5 + 2y) (iii)

Now put the value of x on (i) eq

➝5x + 3y = -11

➝5( - 5 - 2y ) + 3y = -11

➝-25 - 10y + 3y = -11

➝-7y = -11 + 25

➝-7y = 14

➝y = -14/7

➝y = -2

Put the value of y in (iii)eq

➝x = -(5 + 2y )

➝x = -(5 + 2 × -2 )

➝x = - ( 5 - 4 )

➝x = - 1

So we get ( - 1, -2 )

Answer 2

Question:-

• 5x + 3y = - 11 , 2x + 4y = - 10

Solution:-

Here ,

• 5x + 3y = - 11 . . . . . ( 1 )

• 2x + 4y = - 10 . . . . . ( 2 )

Here ,

• Equation ( 1 ) should be multiplied by 2

• Equation ( 2 ) should be multiplied by 5

$\tt\implies \: 2( 5x + 3y = - 11 ) \: \: and \: \: 5( 2x + 4y = - 10 )$

$\tt\implies \: 10x + 6y - 10x - 20y = - 22 + 50$

$\tt\implies \: -14 y = 28$

$\tt\implies \: y = - 2$

Substitute y in equation ( 1 )

$\tt\implies \: 5x + 3y = - 11$

$\tt\implies \: 5x + 3( - 2 ) = - 11$

$\tt\implies \: 5x = - 11 - 6$

$\tt\implies \: x = - 1$