Question

the elimination method and the substitution
1. Solve the following pair of linear equations by the elimination method and
method:
(i) x + y = 5 and 2x – 3y = 4​

Answer 1

Step-by-step explanation:

elimination method;

2x+2y-2x+3y=10-4

5y=6

y=6/5,x=19/5

Answer 2

By elimination method:

The given system of equation is

x + y = 5 ............. ( i )

2x - 3y = 4 ...........( ii )

Multiplying ( i ) by 3 , we get

3( x + y ) = 3 ( 5 )

➠ 3x + 3y = 15 .............( iii )

Adding ( ii ) and ( iii ), we get

( 2x - 3y ) + ( 3x + 3y ) = 4 + 15

➠ 5x = 19

➠ x = 19/5

★ Putting x = 19/5 in equation ( i ) , we get

x + y = 5

➠ 19/5 + y = 5

➠ y = 5 - 19/5

➠ y = (25 - 19 ) / 5

➠ y = 6/5

Hence, x = 19/5 and y = 6/5

By substitution method:

The given system of equation is

x + y = 5 .........( i )

2x - 3y = 4 ........( ii )

y = 5 - x [ from ( i ) ] ........ ( iii )

Substituting y = 5 - x in equation ( ii ) , we get

2x - 3y = 4

➠ 2x - 3( 5 - x ) = 4

➠ 2x - 15 + 3x = 4

➠ 5x = 4 + 15

➠ 5x = 19

➠ x = 19/5

★ Putting x = 19/5 in equation ( i ) , we get

19/5 + y = 5

➠ y = 5 - 19/5

➠ y = ( 25 - 19 ) / 5

➠ y = 6/5

Hence, x = 19/5 and y = 6/5