3. Solve the following simultaneous linear equations.
(i) 15x+6y=7;9y-5x=5
Answers
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Class 10
>>Maths
>>Pair of Linear Equations in Two Variables
>>Algebraic Methods of Solving a Pair of Linear Equations
>>Find whether the following ...
Question
Bookmark
Find whether the following pair of linear equations has a unique solution. If yes, find the solution?
7x−4y=49 and 5x−6y=57
Medium
Solution
verified
Verified by Toppr
We have,
7x−4y=49...(i) and
5x−6y=57...(ii)
Here
a
1
=7,b
1
=−4,c
1
=49 and
a
2
=5,b
2
=−6,c
2
=57
So,
a
2
a
1
=
5
7
,
b
2
b
1
=
−6
−4
=
3
2
Since,
a
2
a
1
=
b
2
b
1
The system has a unique solution.
Now, Multiply equation (i) by 5 and equation (ii) by 7 and subtract,
35x−20y=245
35x−42y=399
22y=−154
⇒y=−7
Put y=−7 in equation (ii)
5x−6(−7)=57
⇒5x=57−42
⇒x=3
Hence x=3 and y=−7