Question

3x-5y=4
9x-2y=7
solve by substitution method ​

Answer 1

Step-by-step explanation:

We have, 3x−5y-4=0

⇒3x−5y=4...(i)

Again 9x=2y+7

⇒9x−2y=7...(ii)

By Elimination Method:

Multiplying equation (i) by 3, we get

9x−15y=12...(iii)

Subtracting (ii) from (iii), we get

9x−15y=12

9x−2y=7

−13y=5

⇒y=−

13

5

Putting the value of equation (ii), we get

9x−2(−

13

5

)=7

⇒9x+

13

10

=7

⇒9x=7−

13

10

⇒9x=

13

91−10

⇒9x=

13

81

⇒x=

13

9

Hence, the required solution is x=

13

9

,y=−

13

5

By Substitution Method:

Expressing x in terms of y from equation (i), we have

x=

3

4+5y

Substituting the value of x in equation (ii), we get

9×(

3

4+5y

)−2y=7

⇒3×(4+5y)−2y=7

⇒12+15y−2y=7

⇒13y=7−12

∴y=−

13

5

Putting the value of y in equation (i), we have

3x−5×(−

13

5

)=4

⇒3x+

13

25

=4

⇒3x=4−

13

25

⇒3x=

13

27

∴x=

13

9

Hence, the required solution is x=

13

9

, y=−

13

5

.

(ii) We have,

2

x

+

2

2y

=−1

⇒

6

3x+4y

=−1

∴3x+4y=−6...(i)

And x−

2

y

=3⇒

3

3x−y

=3

∴3x−y=9...(ii)

By Elimination Method:

Subtracting (ii) from (i), we get

5y=−15 ⇒y=−

5

15

=−3

Putting the value of y in equation (i), we get

3x+r×(−3)=−6

⇒3x−12=−6

⇒3x=−6+12⇒3x=6

Hence, Solution is x=2 , y=−3

By Substitution Method:

Expressing x in terms of y from equation (i), we have

x=

3

−6−4y

Substituting the value of x in equation (ii) from equation (i), we get

3×(

3

−6−4y

)−y=9

⇒−6−4y−y=9

⇒−6−5y=9

⇒−5y=9+6=15

∴y=

−5

15

=−3

Putting the value of y in equation (i), we get

3x+×(−3)=−6

⇒3x−12=−6

⇒3x=12−6=6

∴x=

3

6

=2

Hence, the required solution is x=2,y=−3

Answer 2

Answer:

x = 27/26, y = -5/13

Step-by-step explanation:

Substitution method:

Given pair of equations,

3x-5y = 4

=> 3x = 4+5y ----(1)

and

9x-2y = 7 ----(2)

Substitute equation (1) in equation (2), we get

=> 3(4+5y)-2y = 7

=> 12+15y-2y = 7

=> 13y = 7 - 12

=> 13y = -5

=> y = -5/13

Put y value in equation (1),we get

$3x = 4+5\times \left(\frac{-5}{13}\right)$

$\implies 3x = 4-\frac{25}{13}$

$\implies 3x = \frac{52-25}{13}$

$\implies x = \frac{27}{26}$

Elimination method:

3x-5y = 4 ---(1)

9x -2y = 7 ---(2)

/* multiply equation (1) by 3 , and subtract from equation (2), we get

9x-2y = 7

9x-15y = 12

_______________

0 + 13y = -5

_______________

y = -5/13

/* Substitute y = -5/13 in equation (1) , we get

3x - 5(-5/13)=4

=> 3x +25/13 = 4

=> 3x = 4-(25/13)

=> 3x = (52-25)/13

=> x = 27/26

Therefore,.

x = 27/26, y = -5/13