the pair of equations -x+2y+2=0 and 1/2x-1/4y-1=0 has a unique solution true or false'
Answers
Answer:
True
Step-by-step explanation:
The pair of equation has a unique solution...
Given : a statement : the pair of equations -x+2y+2=0 and 1/2x-1/4y-1=0 has a unique solution
To find : Whether True or False
Solution:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
has unique solution if
a₁/a₂ ≠ b₁/b₂
-x + 2y + 2 = 0
1/2x - 1/4y - 1 = 0
=>a₁/a₂ = -1/(1/2) = -2
b₁/b₂ = 2/(-1/4) = - 1/2
-2 ≠ - 1/2
=> pair of equations -x+2y+2=0 and 1/2x-1/4y-1=0 has a unique solution
Hence True
-x + 2y + 2 = 0
1/2x-1/4y-1=0 => x - y/2 - 2 = 0
Adding both => 3y/2 + 0 = 0
=> y = 0 & x = 2
unique solution ( 2 , 0)
Given Statement is True
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