Question

the system of inequalities in the graph represents the change in an account, y, depending on the days delinquent, x. which symbol could be written in both circles in order to represent this system algebraically? y o x y o -x

Explanation:

Step1: Analyze the boundary lines

The lines \(y = x\) and \(y=-x\) are dashed. For a dashed line \(y = mx + b\), the inequality is either \(y>mx + b\) or \(y

Step2: Test a point in the shaded region

Let's take the point \((1,1)\).
For the line \(y=x\), when \(x = 1,y=1\). Substitute into \(y\) and \(x\). The pink - shaded region (where \((1,1)\) lies) satisfies \(y\geq x\) (but since the line is dashed, we consider the strict inequality). Also, for the line \(y=-x\), when \(x = 1,y=- 1\). Substitute \(x = 1,y = 1\) into \(y\) and \(-x\), we get \(y> - x\).
Let's take another approach. The general rule for a linear inequality \(y\) and \(y=mx + b\):
If the line is dashed (\(y=mx + b\) is not included in the solution set), and we can use the origin \((0,0)\) (if it is not on the line). But in this case, the origin is on both lines \(y=x\) and \(y =-x\).
For the line \(y=x\), pick a point \((2,3)\) in the non - purple region. \(3>2\), so the region above \(y = x\) (dashed) satisfies \(y>x\).
For the line \(y=-x\), pick a point \((2,3)\), \(3>-(- 2)=2\), so \(y>-x\)

Answer:

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