Question

On comparing the ratios `bb(a_1/a_2, b_1/b_2)` and `bb(c_1/c_2)`, find out whether the following pair of linear equations are consistent, or inconsistent. 

`3/2x + 5/3y = 7` ; 9x - 10y = 14

Answer 1

`3/2x + 5/3y = 7`

9x - 10y = 14

`a_1/a_2 = (3/2)/9 = 1/6,`

`b_1/b_2= (5/3)/-10=(-1)/6,`

`c_1/c_2 = 7/14 = 1/2`

Here `a_1/a_2!=b_1/b_2`

∴ `a_1/a_2 ≠ b_1/b_2`

Since `a_1/a_2 ≠ b_1/b_2`, these lines intersect and hence the pair of linear equations is consistent.