When the absolute values of two expressions are equal, either the expressions are equal or the opposite of the expressions are equal. For example, if we have the equation,
|ax+b|=|cx+d|
then we can have either
Expressions are equal:& ax+b=cx+d
Opposite are equal:& ax+b=- (cx+d).
We have the equation |2x-4|=|-5x+1| and asked to write it as two separate systems of equations. First, we can write it as two separate cases as shown above.
2x+4=-5x+1 or 2x+4=- (-5x+1)
We can simplify the second equation a little bit by distributing the negative sign. Then the right-hand side becomes 5x-1. Now, we can allow each side of both equations to be equal to y, then we will have two systems of equations.
2x+4=-5x+1 ⇒ & y=2x+4 y=-5x+1
2x+4=- (-5x+1) ⇒ & y=2x+4 y=5x-1)
