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Solving Systems of Linear Inequalities Graphically

Solving Systems of Linear Inequalities Graphically 1.5 - Solution

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We begin by examining the lines as boundary lines to the shaded region. We see that the edge of the area consists of a vertical line along with the yy-axis, a horizontal line along the xx-axis, and a dashed line. Let's extend these lines.

The horizontal line can be described with the equation y=0y=0 and the vertical line is given by x=0.x=0. To find the equation of the dashed line we can mark the slope and the yy-intercept. Then, the equation can be written in slope-intercept form.

Now we have the equations of the three boundary lines representing the region. The next step is to write inequalities for each equation to form a system of inequalities. We see that the shaded area is below, but not on, the line y=-x+4,y=\text{-} x+4, which means that the first inequality is y<-x+4. y < \text{-} x+4. The area is also located to the right of x=0.x=0. This means it's all xx-values greater than or equal 0.0. x0. x \geq 0. Finally, the area also above, and on, the line y=0.y=0. Together these three inequalities describes the shaded region. {y<-x+4x0y0 \begin{cases}y < \text{-} x+4 \\ x \geq 0 \\ y \geq0 \end{cases}