Question

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qno.10

Answer 1

Answer:

a = 5, b = 1

Step-by-step explanation:

The first equation

2x + 3y = 7        ... (1)

represents a line.

The second equation, rewritten, represents another line

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

There are infinitely many solutions when these two equations represent the same line.  This means that equation (2) would need to be a multiple of equation (1).  So

a - b = 2c            ... (3)

a + b = 3c            ... (4)

3a + b - 2 = 7c       ... (5)

Subtracting (3) from (4) gives

2b = c        ... (6)

Putting this into (3) gives

a = b + 2c = b + 4b = 5b   .... (7)

Putting (6) and (7) into (5) gives

3(5b) + b - 2 = 7(2b)  =>  15b + b - 2 = 14b  =>  2b = 2  =>  b = 1

From (7) we get

a = 5b = 5

Answer 2

Answer:

Step-by-step explanation: