Question : Check whether the given pair of linear equations has unique solution, no solution or infinitely many solutions. In case there is a unique solution, then find it by any algebraic method.
5x-4y+8=0
7x+6y-9=0
Doubt by Saksham
Solution :
5x-4y+8=0
7x+6y-9=0
a1/a2 = 5/7
b1/b2 = -4/6 = -2/3
a1/a2≠b1/b2
a1/a2≠b1/b2
Hence, the given lines has unique solutions.
5x-4y+8=0
5x-4y=-8 — (1)
7x+6y-9=0
7x+6y=9 — (2)
7x+6y=9 — (2)
[5x-4y=-8]×7
[7x+6y=9]×5
35x- 28y=-56
[7x+6y=9]×5
35x- 28y=-56
35x+30y= 45
- - -
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0 - 58y = -101
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-58y=-101
58y = 101
- - -
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0 - 58y = -101
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-58y=-101
58y = 101
y = 101/58
putting in eq (1)
5x-4(101/58)=-8
5x-404/58=-8
5x=-8+(404/58)
5x=(-464+404)/58
5x=(-60/58)
x=(-60/[58×5])
x=-12/58
x=-6/29
5x-404/58=-8
5x=-8+(404/58)
5x=(-464+404)/58
5x=(-60/58)
x=(-60/[58×5])
x=-12/58
x=-6/29
∴ x=-6/29, y=101/58