Answer:
A. [tex]a=10\\ \\b\neq -8[/tex]
B. [tex]a=10\\ \\b= -8[/tex]
Step-by-step explanation:
Consider the equation
[tex]2(5x-4) = ax + b[/tex]
A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.
First, use distributive property:
[tex]2(5x-4)=2\cdot 5x-2\cdot 4=10x-8[/tex]
So, the equation is
[tex]10x-8=ax+b[/tex]
This equation has no solutions when
[tex]a=10\\ \\b\neq -8[/tex]
B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.
So, the equation
[tex]10x-8=ax+b[/tex]
has infinitely many solutions when
[tex]a=10\\ \\b= -8[/tex]
In other cases, the equation has a unique solution
