Question

Check wether the pair of linear equation x+3y-6=0 and 2x+17y-30=0 is consistent

Answer 1

A pair of linear equation is said to be consistent if it has atleast one solution.

Given two equations -

x + 3y - 6 = 0

2x + 17y - 30 = 0

Here,

$\mathsf{a_1}$ = 1

$\mathsf{a_2}$ = 2

$\mathsf{b_1}$ = 3

$\mathsf{b_2}$ = 17

$\mathsf{c_1}$ = - 6

$\mathsf{c_2}$ = - 30

Now,

1 / 2 ≠ 3 / 17

$\mathsf{a_1 \ / \ a_2}$ ≠ $\mathsf{b_1 \ / \ b_2}$

This shows that the lines are intersecting.

Hence, this pair has one solution.

•°• It is consistent.

^^"