Question

(2x+y/2) (2x/3+2y+5/2) y+5x/3+1/2 solve using elimination method​

Answer 1

Step-by-step explanation:

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

2x−3y=4 ...(ii) (elimination method)

Multiply eqn (i) by 2

2x+2y=10

2x−3y=4

−+−

____________

5y=6

⇒y=

5

6

Substitute y=

5

6

in eqn (i)

x+y=5

x+

5

6

=5

⇒x=

5

5×5

−

5

6

=

5

19

Substitution method

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

2x−3y=4 ....(ii)

y=5−x ...(iii)

Putting eqn. (3) in (2)

2x−3(5−x)=4

2x−15+3x=4

x=

5

19

y=

5

5×5

−

5

19

y=

5

6

(ii)

Elimination method

3x+4y=10 ...(i)

2x−2y=2 ...(ii)

Multiply eqn (2) by 2

4x−4y=4

3x+4y=10

____________

7x=14

x=2

2×2−2y=2

⇒4−2=2y

y=1

Substitution method

3x+4y=10 ...(i)

2x−2y=2⇒x−y=1

x−1=y ...(ii)

Putting eqn (ii) in (i)

3x+4(x−1)=10

3x+4x−4=10

_________________

7x=14

x=2

y=x−1

y=2−1

⇒y=1

(iii) 3x−5y=4 ...(i)

9x−2y=7 ...(ii) (elimination method)

Multiply eqn (i) by 3

(ii)-(i)×3

9x−2y=7

9x−15y=12

_____________

13y=−5

⇒y=

13

−5

3x−5×

13

−5

=4

⇒3x=4−

13

25

3x=

13

52−25

x=

13×3

27

⇒x=

13

9

Substitution method

3x−5y=4 ...(i)

9x−2y=7

⇒9x−7=2y

2

9x−7

=y

3x−5y=4

⇒3x−5(

2

9x−7

)=4

⇒3x−

2

45

x+

2

35

=4

⇒

2

6x

−

2

45

x=4−

2

35

⇒

2

−39x

=

2

8−35

x=

39

27

⇒x=

13

9

Putting x=

13

9

in 3x−5y=4

13

3×9

−5y=4

13

27

−5y=4

⇒

13

27

−4=5y

⇒

13

27−52

=5y

13

−25

=5y

⇒y=

13

−5

(iv)Elimination method

2

x

+

3

2y

=−1

6

3x+4y

=−1

⇒3x+4y=−6 ...(i)

x−

3

y

=3

⇒3x−y=9 ...(ii)

(i)−(ii)

3x+4y=−6

3x−y=−9

−+−

______________

5y=−15

⇒y=−3

Putting y=−3 in eqn (i)

3x−12=−6

⇒3x=−6+12

⇒3x=6

⇒x=2

Substitution method

3x+4y=−6 ...(i)

3x−y=9 ...(ii)

3x−9=y ....(iii)

Putting enq (iii) in (i)

3x+4(3x−9)=−6

⇒3x+12x−36=−6

⇒15x=−6+36

⇒15x=30

⇒x=2

Putting x=2 in eq (iii)

6−9=y

⇒y=−3