a must be greater than zero and b must be less than zero.
Here we have the following system of inequalities:
[tex]\left.\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y<-x+a\\y>x+b\end{array}\right.\right.[/tex]
Given that the origin is a solution to the system, then by substituting [tex]x=0 \ and \ y=0[/tex] into each inequality we'll get the relationship for both a and b:
[tex]\left.\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}0<-(0)+a\\0>0+b\end{array}\right.\right. \\ \\ \\\left.\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}0<a\\0>b\end{array}\right.\right. \\ \\ \\\left.\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}a>0\\b<0\end{array}\right.\right.[/tex]
So finally, the conclusion is that a must be greater than zero and b must be less than zero.
Inequalities: https://brainly.com/question/12890742
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