the system of linear equations 2x + 3y + a = 0 and 3x + 4.5y + b = 0, where b is 1 more than a and the sum of a, b is 5, has _____ solution(s)
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
see in pair of linear eqn in 2 variables we have studied that if
a1/a2=b1/b2=c1/c2 then the 2 equations have infinitely many sol.
here on putting this eqn in the form of a1/a2=b1/b2=c1/c2 we get 2/3=2/3 =a/b
also its given b = a+1
and a+b=5
i.e a+(a+1) =5
a=2 on solving similarly b=3
and 2/3=2/3 =a/b so 2/3=2/3=2/3 hence we satisfy the condition for infinitely many sol.
hope u understood!!
Given : system of linear equations 2x + 3y + a = 0 and 3x + 4.5y + b = 0, where b is 1 more than a and the sum of a, b is 5
To find : number of Solutions
Solution:
2x + 3y + a = 0
3x + 4.5y + b = 0
b is 1 more than a and the sum of a, b is 5
=> b = a + 1
a + b = 5
=> a + a + 1 = 5
=> 2a = 4
=> a = 2
& b = 3
2x + 3y + 2 = 0
3x + 4.5y + 3 = 0
2/3 = 3/4.5 = 2/3
=> 2/3 = 2/3 = 2/3
hence both lines coincide
hence infinite Solution
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