In the xy-plane, if (0,0) is a solution to the inequalities above, which of the following relationships between a+b must be true

Respuesta :

  • [tex]a[/tex] must be greater than zero
  • [tex]b[/tex] must be less than zero

Explanation:

The complete question is written in a comment above. The system of inequalities is the following:

[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y<-x+a\\y>x+b\end{array}\right.[/tex]

So, in order to find [tex]a \ and \b[/tex] you just need to replace both x and y-coordinates into our system. Therefore:

[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}0<-0+a\\0>0+b\end{array}\right. \\ \\ \\ Solving: \\ \\ \begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}0<a\\0>b\end{array}\right. \\ \\ \\ Finally: \\ \\ \begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}a>0\\b<0\end{array}\right.[/tex]

So the conclusion is:

  • [tex]a[/tex] must be greater than zero
  • [tex]b[/tex] must be less than zero

Learn more:

Inequalities: https://brainly.com/question/12890742

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