Question

5. Check whether the pair of linear equations:
2x + 3y = 5 and 4z + 6y = 10 is consistent or not?​

Answer 1

• Explanation for how to solve the question: Attachment 01
• Answer to the question: Attachment 02

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Answer 2

$\sf\huge {\underline{\underline{{Solution}}}}$

2x+3y=5-----(1)

4x+6y=10----(2)

Now, compare both Equation :

a₁ = 2,a₂= 4

b₁= 3,b₂= 6

c₁ = 5,c₂= 10

To check whether the pair of linear equations is consistent or not :

a₁ / ,a₂ = 2/4= 1/2

b₁/b₂= 3/6= 1/2

c₁ / c₂= 5/10= 1/2

Since , a₁ / ,a₂ =b₁/b₂= c₁ / c₂ So, therefore given pair of linear equations is consistent and has infinitely many solutions.

Extra information=>

• If a given pair of linear equations have unique solution then : a₁ / ,a₂ ≠ b₁/b₂
• If a given pair of linear equations have no solution then : a₁ / ,a₂ ≠ b₁/b₂ ≠ c₁ / c₂
• The graph of the unique solution be a straight lines.
• The graph of the no solution is Parallel lines .
• The graph of the infinite solutions is coincident lines.