Question

3x-5y-4=0 and 9x=2y+7​

Answer 1

Answer:

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

.