Question

solve : 2x+y=12 and x+2y = 9​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

Above given Equation can be solved in various ways.Here, we solve through substitution method and elimination method:

By substitution method

=> 2x+y= 12------(1)

=> x+2y= 9-------(2)

From equation 1

=> y= 12-2x----(3)

Put y in Equation 2

=> x+2(12-2x)=9

=> x+24-4x= 9

=> -3x+24=9

=> -3x = 9-24

=> -3x= -15

=> 3x= 15

x= 5

Put x into Equation 3

=> y= 12-2x

=>y= 12-2(5)

=> y= 12-10

y= 2

Check:

=> 2x+y= 12

=> 2(5)+2

=> 10+2

=12

Since,LHS = RHS (Verified)

Alternative Method

By elimination method

=> 2x+y= 12---× 1

=> x+2y=9-----×2

New Equation obtained

=> 2x+y=12

=> 2x+4y=18

=>$(-)(-)\:(-)$

___________

-3y= -6

y=2

=>2x+y=12

=> 2x+2=12

=>2x=12-2

=>2x= 10

x=5

Answer 2

$\underbrace \mathscr \red{Answer}$

Above given Equation can be solved in various ways.Here, we solve through substitution method and elimination method:

By substitution method

=> 2x+y= 12------(1)

=> x+2y= 9-------(2)

From equation 1

=> y= 12-2x----(3)

Put y in Equation 2

=> x+2(12-2x)=9

=> x+24-4x= 9

=> -3x+24=9

=> -3x = 9-24

=> -3x= -15

=> 3x= 15

x= 5

Put x into Equation 3

=> y= 12-2x

=>y= 12-2(5)

=> y= 12-10

y= 2

Check:

=> 2x+y= 12

=> 2(5)+2

=> 10+2

=12

Since,LHS = RHS (Verified)

By elimination method

=> 2x+y= 12---× 1

=> x+2y=9-----×2

New Equation obtained

=> 2x+y=12

=> 2x+4y=18

=>(-)(-)\:(-)(−)(−)(−)

___________

-3y= -6

y=2

=>2x+y=12

=> 2x+2=12

=>2x=12-2

=>2x= 10

x=5