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Question

Show that each of the following systems of equations has a unique solution and solve it:

3x+5y=12,5x+3y=4.


Solution

3x+5y12=0,

5x+3y4=0

a1=3,b1=5,c1=12

a2=5,b2=3,c2=4

Thus,

a1a2b1b2

Hence, the given system of equations has a unique solution.

The given equations are,

3x+5y=12.....(1)

5x+3y=4.......(2)

Multiplying (1) by 3, and (2) by 5, we get

9x+15y=36......(3)

25x+15y=20......(4)

Subtracting (3) from (4), we get

16x=16

x=1616=1

x=1

Putting x = -1 in (3), we get

(9)(1)+15y=36

9+15y=36

15y=36+9

y=4515=3

Hence, the solution is x=1,y=3

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