Question

Which of the following pairs of linear equations has unique solution, infinitely many
solutions or no solution? In case there is a unique solution, find it by using cross-
multiplication method:
1)3x + 2y = 4
8x+5y=9
2)3x-7y+10=0
y-2x=3
3)3x-4y=7
15x-20y=21
4)7y-2x=5
21y-6x=15

Answer 1

Answer:

Only 1) and 2) have unique solution, as for them a1/a2 ≠ b1/b2.

For 3), a1/a2 = b1/b2 ≠ c1/c2. Hence it has no solution.

And in 4), a1/a2 = b1/b2 = c1/c2. So, it has infinitely many solutions.

Now,

Solving (i)

1) 3x + 2y = 4  => 3x + 2y - 4 = 0

 8x + 5y = 9  => 8x + 5y - 9 = 0

∴ x/ 2*(-9) - (-4)*5 = y/(-4)*8 - 3*(-9) = 1/3*5 - 2*8

=> x/2 = y/-5 = -1

x = -2, y = 5

Solving (ii)

2)                        3x - 7y + 10 = 0  

     y - 2x = 3 => -2x + y - 3 = 0

∴ x/ (-7)*(-3) - 10*1 = y/(-2)*10 - 3*(-3) = 1/3*1 - (-2)*(-7)

=> x/11 = y/-11 = 1/-11

x = -1, y = 1.