Question

do the following equation represent a pair of coincident lines 4x+3y-1=0, 12x+9y=15​

Answer 1

Answer:

Yes

Step-by-step explanation:

The 2 given linear equations in 2 variables are:

• 4x + 3y - 1 = 0
• 12x + 9y - 15 = 0

For lines to be coincident,

$\tt{\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2} }$

Here,

$\tt{ \dfrac{4}{12} = \dfrac{3}{9} \neq \dfrac{ - 1}{15} }$

Further simplifying,

$\tt{\dfrac{1}{3} = \dfrac{1}{3} \neq \dfrac{ - 1}{15} }$

So, the given pair of linear equations would represent coincident lines on a graph paper

KNOW MORE:

• For parallel lines,

(a₁ ÷ a₂) = (b₁ ÷ b₂) = (c₁ ÷ c₂)

• For intersecting lines,

(a₁ ÷ a₂) ≠ (b₁ ÷ b₂) ≠ (c₁ ÷ c₂)