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The system of equations below is consistents with infinity many solutions where a and b are constants.Find the values of a and b. 2x+y=6 ax+by=9

User Majid Sadr
by
8.1k points

1 Answer

4 votes

Answer:

The values of
a and
b so that the two linear equations have infinite solutions are
3 and
(3)/(2), respectively.

Explanation:

Two linear equations with two variables have infinite solution if and only if they are linearly dependent. That is, one linear equation is a multiple of the other one. Let be the following system of linear equations:


2\cdot x + y = 6 (1)


a\cdot x + b\cdot y = 9 (2)

The following condition must be observed:


r = (a)/(2) = (b)/(1) = (9)/(6) (3)

After some quick operations, we find the following information:


r = (3)/(2),
a = 3,
b = (3)/(2)

The values of
a and
b so that the two linear equations have infinite solutions are
3 and
(3)/(2), respectively.

User Masoud Keshavarz
by
8.5k points

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