Question

3. The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have
(a)Unique solution
O (b)Exactly two solutions
O (c)Infinitely many solutions
0
(d)No solution
O Other​

Answer 1

Answer:

It will have no solution as the lines are parallel and when the lines are parallel there is no solution

Answer 2

Answer:

The pair of linear equations  9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have no solution.

Step-by-step explanation:

Recall the concepts

A pair of linear equations $a_1x + b_1y + c_1 = 0 \ and \ a_2x + b_2y + c_2 = 0$ have

1. exactly one solution if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$
2. infinitely many solutions if $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
3. no solution if $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$

Given equations are 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0

Comparing with  $a_1x + b_1y + c_1 = 0 \ and \ a_2x + b_2y + c_2 = 0$ we get

$a_1 = 9 , b_1 = 3, c_1 = 12 \ and \ a_2 = 18, b_2 = 6 ,c_2 = 26$

$\frac{a_1}{a_2} = \frac{9}{18} = \frac{1}{2}$

$\frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2}$

$\frac{c_1}{c_2} = \frac{12}{26}$

Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,  the pair of linear equations  9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have no solution.

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