Question

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Answer 1

Answer:

No Solution

Step-by-step explanation:

Let us see the various conditions to check the number of solutions for a pair of linear equations.

Let our linear equations are

ax+by=c

px+qy=r

i) for Unique Solution

$\frac{a}{p}$ ≠ $\frac{b}{q}$ = $\frac{c}{r}$

$\frac{a}{p}$ ≠ $\frac{b}{q}$ ≠ $\frac{c}{r}$

ii) For No Solution

$\frac{a}{p}$ = $\frac{b}{q}$ ≠ $\frac{c}{r}$

iii) For many Solutions

$\frac{a}{p}$ ≠ $\frac{b}{q}$ = $\frac{c}{r}$

Let us see what ratio we have for our linear equation s

here

a=1 , b=-2 , c= 4

p=-3 , q = 6 , r = 12

$\frac{a}{p}$ = $\frac{1}{-3}$ = - $\frac{1}{3}$

$\frac{b}{q}$ = $\frac{-2}{6}$ = - $\frac{1}{3}$

$\frac{c}{r}$ = $\frac{4}{12}$ =  $\frac{1}{3}$

- $\frac{1}{3}$ =  - $\frac{1}{3}$ ≠ $\frac{1}{3}$

Hence it satisfies the second condition of No solution