Question

4. For what values of a and b does the following
pair of linear equations have infinitely many
solutions ?
2x + 3y = 7
a (x + y) - b (x - y) = 3a + b -2
​

Answer 1

Answer:

a=5 b=1

Step-by-step explanation:

Firstly We represent 2nd Equation as ax +by+c=0

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• •

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

ax+ay-bx+by=3a+b-2

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

Also We have,

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

For Infinite Solutions For Eqn(1) and Eqn(2),

a1/a2=b1/b2=c1/c2

Substitute The Values From Eqn(1) and Eqn (2),

we have,

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

From 1st Equality,

3a-3b=2a+2b

a=5b.............. (3)

Now, From 2nd Equality,

a+b/3=3a+b-2/7

Putting The Value Of a from Eqn(3),

5b+b/3=3×5b+b-2/7

2b=16b-2/7

14b=16b-2

-2b=-2

b=1............ (4)

And Using Eqn(3),

We Have,

a=5b

a=5 [since b=1 From Eqn(4) ]

Therefore

For a=5 and b=1

The given Line Pairs Have Infinite Solutions.