Question

Consider the equation

Answer 1

Answer:

A. $a=10\\ \\b\neq -8$

B. $a=10\\ \\b= -8$

Step-by-step explanation:

Consider the equation

$2(5x-4) = ax + b$

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:

$2(5x-4)=2\cdot 5x-2\cdot 4=10x-8$

So, the equation is

$10x-8=ax+b$

This equation has no solutions when

$a=10\\ \\b\neq -8$

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

$10x-8=ax+b$

has infinitely many solutions when

$a=10\\ \\b= -8$

In other cases, the equation has a unique solution