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Solving Linear Systems

Solving Linear Systems 1.8 - 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 -axis, a horizontal line along the -axis, and a dashed line. Let's extend these lines.

The horizontal line can be described with the equation and the vertical line is given by To find the equation of the dashed line we can mark the slope and the -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 which means that the first inequality is The area is also located to the right of This means it's all -values greater than or equal Finally, the area also above, and on, the line Together these three inequalities describes the shaded region.