Q2 of 244 Page 124

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

2x - 3y = 17, 4x + y = 13.

Given: 2x – 3y = 17 – eq 1


4x + y = 13 – eq 2


Here,


a1 = 2, b1 = - 3, c1 = 17


a2 = 4, b2 = 1, c2 = 13


= , =


Here, ≠


∴ Given system of equations have unique solutions.


Now,


In – eq 1


2x = 17 + 3y


X =


Substitute x in – eq 2


we get,


4× + y = 13


= 13


68 + 12y + 2y = 26


68 + 14y = 26


14y = 26 – 68


14y = - 42


y = = - 3


∴ y = - 3


Now, substitute y in – eq 1


We get,


2x – 3×( - 3) = 17


2x + 9 = 17


2x = 17 – 9


2x = 8


x = 8/2 = 4


∴ x = 4


∴ x = 4 and y = - 3


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