Question

The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:

(A) A unique solution                        

(B) Exactly two solutions

(C) Infinitely many solutions             

(D) No solution


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Answer 1

Answer:

(C) infinitely many solutions

Step-by-step explanation:

The pair of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 have

1) no solution when   $\rm \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$  

2) infinite solutions when   $\rm \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$  

3) unique solution when   $\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$

Given pair of equations,

x + 2y – 5 = 0

−3x – 6y + 15 = 0

Comparing the given two equations with a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, we get  

a₁ = 1 , b₁ = 2 , c₁ = -5  

a₂ = -3 , b₂ = -6 , c₂ = 15

a₁/a₂ = 1/-3 = -1/3

b₁/b₂ = 2/-6 = -1/3

c₁/c₂ = -5/15 = -1/3

a₁/a₂ = b₁/b₂ = c₁/c₂

Hence, the given pair of equations have infinitely many solutions.

Answer 2

Answer:

Infinitely many solutions

Step-by-step explanation:

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