Question

The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have

Answer 1

9x=-12-3y

x=(-12-3y)/9

18x+6y+24=0

18 (-12-3y)+6y+24=0

-216-54y+6y+24=0

-192-48y=0

-48y=192

y=-192/48=-4

so y=-4

then,

x=(-12-3y)/9=[-12-(3×-4)]/12=(-12+12)/12=0/12=0

so x=0 ; y= -4

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Answer 2

Concept: The general representation of linear pair in two variables are:

a1x+b1y+c1=0

a2x+b2y+c2=0

The pair of linear equations may be consistent or inconsistent.

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

Find: Find the pairs of equations.

Solution: In these equations

a1=9  b1=3  c1=12

a2=18  b2=6  c2=26

$\frac{a1}{a2}=\frac{9}{18}=\frac{1}{2}$

$\frac{b1}{b2} =\frac{3}{6} =\frac{1}{2}$

$\frac{c1}{c2} =\frac{12}{26} =\frac{6}{13}$

$\frac{a1}{a2}$=$\frac{b1}{b2}$≠$\frac{c1}{c2}$

∴ The pair of linear equation is inconsistent and the graph are parallel.

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