"Which points are in the solution set?" The system of linear inequalities are, y<1/2x-1 and y greater than or equal to 2x+3. How would I find the points?

Answer 1

Hi Dayna,

Your question does not show any points to pick from, so I am assuming you are supposed to do what is typical for a problem like this->draw a graph to show the solution set.

https://www.desmos.com/calculator/draudgi0i7

1. Draw a border for each region [y= 1/2 (x) -1; this will be a dotted border because there is no "equal sign for the inequality; y = 2x+3; solid border]
2. Shade in the side of the border that gives a true statement. Typically we substitute (0,0), x=0, y=0 into the inequality--if a true statement is revealed, then shade in that side of the border, otherwise the other side.
3. Where the two regions overlap--that represents the solution set for the system of inequalities.
4. In the referenced graph (-8,-6) is one of infinitely many ordered pairs that make the system of inequalities true. The point (-6,-1) makes one of them true, but not the other. Same for (4,-2). Finally the point (1,1) or even (0,0) does not make either of them true.

Hopefully you understand how to draw the border. These are in slope intercept form.

Answer 2

This is going to be answered by graphing. You need to graph the linear equation (1/2)x-1 as a dotted line because the points that lie on this line are not included because of the "less than" criteria and everything below this line is to be shaded which represents all the points that are solutions to this equation. Next, you need to graph the linear equation 2x+3 as a solid line because all the points that lie on this line are included because of the "greater than or equal to" criteria and everything above it needs to be shaded to represent all the points that are solutions to this equation. Where the two shaded areas overlap will be the solution set for both equations.