Question

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✍✍ For which values of a and b does the following pair of linear equations have an infinite number of solutions ?

2x +3y = 7
(a - b ) x+( a+b ) y = 3a + b- 2

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@Brainlestuser

Brainly Team , Moderator

Answer 1

Hope this hlp..........

Answer 2

APPROACH TO PROBLEM:
To find values of a and b:
1. Compare given pair of linear equations (in two variables) with the general form.
2.Find the coefficients a1, b1, c1 & a2,b2,c2
3. The given pair of linear equations are said to have infinite no. of solutions if and only if
a1/a2 = b1/b2 = c1/c2.
Then solve for a and b

•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°•°

SOLUTION:

The given pair of linear equations are:

2x+3y- 7 = 0---------------------(1)
(a-b)x + (a+b)y -(3a+b-2) = 0 ------(2)

The general form of pair of linear equation are given as:
a1 x + b1 y + c1= 0 --------------(3)
a2 x + b2y + c2= 0 -------------(4)

Comparing coefficients of (1) and (3)
we get,
a1= 2
b1= 3 and
c1= 7

//y compare (2) and (4),
a2= (a-b)
b2= (a+b) and
c2= -(3a+b-2)

As per the given data,
the pair of equations are said to have infinitely many solutions

•°• a1/a2 = b1/b2 = c1/c2

Substitute values in the above .
we get,

2/(a-b) = 3/(a+b) = -7/-(3a+b-2)
2/(a-b) = 3/(a+b) = 7/(3a+b-2) -----(5)

Now, solve for a and b

Equate first and second terms of (5)
2/(a-b) = 3/(a+b)
Cross multiply
2(a+b) = 3(a-b)
=>2a+2b= 3a- 3b
=>3b+2b= 3a-2a
=>5b = a -------------------(6)

Equate first and third terms of (5)
2/(a-b) = 7/(3a+2b-2)
Cross Multiply
2(3a+b-2) = 7(a-b)
=>6a+2b-4 = 7a-7b
=>7b+2b-4=7a-6a
=> 9b-4 = a ---------------------(7)

Equate (6) & (7). We get,
5b = 9b-4
=>9b-5b= 4
=> 4b= 4
=> b= 1

From(6) we have,
a= 5b
substitute b= 1 in above equation
a= 5(1)
=> a= 5

•°• If a= 5 and b= 1, the given pair of linear equations have infinite no. of solutions.

;)
Hope it helps