Hard SAT and ACT Math Problem with Solution System of Inequalities Today I would like to provide a solution to yesterday’s SAT/ACT problem involving a system of inequalities. Here is the problem once again, followed by a solution. Level 5 System of Inequalities y ≤ 2x + 2 y ≥ –3x – 3 A system of inequalities and a graph are shown above (the graph is at the top of the post). Which section or sections of the graph could represent all of the solutions to the system? A. Section I B. Section IV C. Sections II and III D. Sections II and IV E. Sections I, II and IV Solution: The line y = 2x + 2 has a slope of 2 > 0, and therefore the graph is the line that moves upwards as it is drawn from left to right. The point (0,0) satisfies the inequality y ≤ 2x + 2 since 0 ≤ 2(0) + 2, or equivalently 0 ≤ 2 is true. It follows that the graph of y ≤ 2x + 2 consists of sections II and IV. The line y = –3x – 3 has a slope of –3 < 0, and therefore the graph is a line that moves downwards as it is drawn from left to right. (0,0) satisfies the inequality y ≥ –3x – 3 since 0 ≥ –3(0) – 3, or equivalently 0 ≥ –3 is true. It follows that the graph of y ≥ –3x – 3 consists of sections III and IV. The intersection of the two solution graphs is section IV, choice B. Note: For a more detailed explanation, see 28 New SAT Math Lessons – Advanced Course More SAT and ACT Math Problems with Explanations If you are preparing for the SAT or ACT, you may want to take a look at the Get 800 collection of test prep books. And if you liked this article, please share it with your Facebook friends: Comments comments