Answer:
The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.
Step-by-step 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:
[tex]2\cdot x + y = 6[/tex] (1)
[tex]a\cdot x + b\cdot y = 9[/tex] (2)
The following condition must be observed:
[tex]r = \frac{a}{2} = \frac{b}{1} = \frac{9}{6}[/tex] (3)
After some quick operations, we find the following information:
[tex]r = \frac{3}{2}[/tex], [tex]a = 3[/tex], [tex]b = \frac{3}{2}[/tex]
The values of [tex]a[/tex] and [tex]b[/tex] so that the two linear equations have infinite solutions are [tex]3[/tex] and [tex]\frac{3}{2}[/tex], respectively.
