3x-5y=4 , 9x-2y=7 solve the equation linear equations in two variables
Answers
Answer:
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
.