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TOPIC 3: Linear Equations and Inequalities 1. Solve: 2x 4 2 . x6 15 2. Solve for the common solutions by substitution or linear combinations. State whether the lines are parallel, perpendicular, intersecting but not perpendicular, or the same line. x y 5 2 x y 1 3. Solve for the common solutions by substitution or linear combinations. State whether the lines are parallel, perpendicular, intersecting but not perpendicular, or the same line. 2 x y 3 4 x 6 2 y 4. Find the slope and the y-intercept. Then sketch the graph: 3x 2 y 6 . 5. Find an equation of the line through (– 3, – 5) and (2, – 2). 6. Graph and write an equation for the vertical line through the point (– 2, 3). 7. Solve and graph on the number line: 2 x 3 9 . 8. Solve the inequality: 2 x 3 y 12 , and shade the solutions on the graph provided. 9. Solve and graph on the number line: 3 5 x 2 . 10. Solve and graph on the number line: 1 2 x 7 . 1 ANSWERS TOPIC 3: Linear Equations and Inequalities 1. x 7. x 3 3 2 2. (– 6, – 11); The lines are intersecting but not perpendicular. 3. When you solve this system, you will get an equation that is true always, such as 0 = 0 or something similar. The lines are the same line, and any solution to the line will be a solution to the system. Writing x, y | 2 x y 3 or x, y | 4 x 6 2 y are equivalent ways to write all solutions. 4. Slope is 8. 3 ; y-intercept = (0,– 3) 2 9. x 1 or x 1 5 0 1 5 2 5 3 5 4 5 1 10. x 3 or x 4 5. y 6. 3 3 16 or y 2 x 2 x 5 5 5 x 2 For more examples, click here 2