Q. 14.2( 9 Votes )
Show that each of the following systems of equations has a unique solution and solve it:
3x + 5y = 12, 5x + 3y = 4.
Answer :
Given: 3x + 5y = 12 – eq 1
5x + 3y = 4 – eq 2
Here,
a1 = 3, b1 = 5, c1 = - 12
a2 = 5, b2 = 3, c2 = - 4
= 
, 
= 
Here, 
≠ 
∴ given system of equations have unique solutions.
Now,
In – eq 1
3x = 12 – 5y
X = 
Substitute x in – eq 2
we get,
5× 
+ 3y = 4
= 4
60 – 25y + 9y = 12
60 – 16y = 12
16y = 60 – 12
16y = 48
y = 
= 3
∴ y = 3
Now, substitute y in – eq 1
We get,
3x + 5×3 = 12
3x + 15 = 12
3x = 12 – 15
3x = - 3
x = 
= - 1
∴ x = - 1
∴ x = - 1 and y = 3
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