find a and b for which the following system of linear equation has infinite number of solutions
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find a and b for which the following system of linear equation has infinite number of solutions
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Verified answer
Answer:
a = 7
b = 3
Step-by-step explanation:
Given a pair of linear equations such that,
2x - (a-4)y = 2b + 1 .......(1)
4x - (a-1)y = 5b - 1 ........(2)
Also, given that,
They have infinite number of solutions.
To find the value of a and b.
We know that,
For infinite solutions,
Substituting the values, we get,
=> 2/4 = -(a-4)/-(a-1) = (2b+1)/(5b-1)
=> 1/2 = (a-4)/(a-1) = (2b+1)/(5b-1)
Here, we have,
=> (a-4)/(a-1) = 1/2
=> 2(a-4) = a-1
=> 2a - 8 = a - 1
=> 2a - a = 8-1
=> a = 7
And
=> (2b+1)/(5b-1) = 1/2
=> 2(2b+1) = 5b-1
=> 4b + 2 = 5b - 1
=> 5b-4b = 2+1
=> b = 3
Hence, required values of a = 7 and b = 3.