In Exercises 27–62, graph the solution set of each system of ineq...

Question

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+y>4, x+y<−1

Accepted Answer

Consider the following system of inequalities. Negative two X plus Y is greater than six. Negative two X plus Y is less than negative four. Now it says the graphics solution said or say that there is no solution. So I graphed it here on the right. Mhm. You notice here, I could have found these lines by finding the intercepts. So for example, if I said negative two X plus Y is greater than six. We replace our greater than with the equal sign to find their intercepts A set Y equal zero. For example, get negative two, X plus zero is equal six or negative two X equals six, dividing both sides by negative two gives us X equals negative three or a point At -30. Which we can see right here on the graph with plug in zero for X. We will get our Y intercept being six. We do the same for our autograph. Getting a Y intercept zero, x intercept of 20. Now the answer to the system and inequalities would be the area where the regions are shaded at the same time. We've noticed here we don't have an area where they're both shaded for this graph. The areas shaded above. So it always goes up with the wrong and the right areas shaded below. So it always goes down because they don't have any overlapping areas shaded. We can go ahead and say that we have no solution or answer D. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye