Answer: a= -3 and b=2.
Step-by-step explanation:
If a system of linear equations has infinitely many solutions, then
Ratio of coefficient of y= ratio of coefficient of x = ratio of constants.
Given system: [tex]y=2x+a[/tex]
[tex]y=bx-3[/tex]
It it has infinitely many solutions, then
[tex]\dfrac{1}{1}=\dfrac{2}{b}=\dfrac{a}{-3}\\\\\Rightarrow\ \dfrac{2}{b}=1\ \ \ \text{ and }\ \ \dfrac{a}{-3}=1\\\\\Rightarrow\ b=2\ \ \ \text{ and } \ \ a=-3[/tex]
hence, a= -3 and b=2.
