Question

The graph of a system of inequalities is shown.Which system is represented by the graph?O y> 2xx+2ys-8Omy 2xx+2y <-8y< 2xx+2y2-8O ys 2xx+2y > -8

Answer 1

we need to find the equations of the lines that separates the plane. The red line has a y-intercept -4 and for every 2 units to the right it decreases 1 unit, then the slope is -1/2. So, the equation of the red line is

`y=-(1)/(2)x-4`

The dashed line passes through the origin, so the y-intercept is 0, also, for every 1 unit to the right it increases 2 units, then the slope is 2 and the equation is

`y=2x`

Finally, we see that the red region is below the the red line and it includes de red line, and the blue region is above the blue line and it doues not include the line, so the inequalities are

`\begin{gathered} y\leq-(1)/(2)x-4 \\ y>2x \end{gathered}`

multiplying the first inequality by 2

`\begin{gathered} 2y\leq-x-8 \\ y>2x \\ x_{}+2y\leq-8 \end{gathered}`

Then, the correct answer is the first one

`\begin{gathered} y>2x \\ x+2y\leq-8 \end{gathered}`