Question

3. A pair of Lincar equations which satisfies dependent system
A) 2x -y-5=0; 3x - 2y - 4 = 0
B) 3x + 4y = 2 : 6r+8y=4
C) x +2y=3 : 2x + 4y = 5
D) x + 2y - 30 = 0 ; 3x + 6y + 60 = 0​

Answer 1

Answer:

B). consistent dependent system.

Step-by-step explanation:

If a system has at least one solution, it is said to be consistent . ... If a consistent system has an infinite number of solutions, it is dependent and both equations represent the same line. If a system has no solution, it is said to be inconsistent.

In consistent dependent system of equations slopes are equal and y-intercepts are the same. Let' solve equations for "y"

A). y = 2x + 5 and y = (3/2)x - 2, a system has one solution.

B). y = (- 3/4)x + (1/2) and y = (- 3/4)x + (1/2), system has infinitely many solutions

C). y = (-1/2)x + (3/2) and y = (-1/2)x + (5/4), system has no solution

D). y = (-1/2)x +15 and y = (-1/2)x - 10, system has no solution

Answer 2

Given :  Four Pair of linear Equations

To find : which pair satisfies dependent system

Solution:

A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions

that means two lines satisfies dependent System

if  a₁x + b₁y + c₁y = 0

 & a₂ + b₂y + c₂y = 0

Satisfies  a₁/a₂ = b₁/b₂ = c₁/c₂

Lets check Each given pair

A) 2x -y-5=0; 3x - 2y - 4 = 0

2/3  ≠ 1/2 ≠ 5/4    ( hence Consistent but not dependent)

B) 3x + 4y = 2 ,  6x + 8y = 4

3/6  = 4/8 = 2/4  = 1/2  

Hence Dependent System

C) x +2y=3 : 2x + 4y = 5

1/2 = 2/4  ≠ 3/5   ( inconsistent System )

D) x + 2y - 30 = 0 ; 3x + 6y + 60 = 0​

1/3  = 1/2  ≠  -1/2   ( inconsistent System )

3x + 4y = 2 ,  6x + 8y = 4 is dependent System

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