MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

Transcription

1 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) A SYSTEM OF LINEAR INEQUALITIES = a problem where or more inequalities are graphed on the same grid, the solution of which is the overlapping shaded area. GRAPHING SYSTEMS OF LINEAR INEQUALITIES I) Sstems of linear inequalities are questions that require ou to graph more than one inequalit on the same grid. This results in an area on the grid where the shaded area of each inequalit overlap. This is the solution to the problem. A) USE THESE STEPS TO SOLVE REAL LIFE SITUATIONS INVOLVING LINEAR INEQUALITIES variables is anthing other than real numbers. B) SAMPLE PROBLEMS 1: Stud these eamples carefull. Be sure ou understand and memorize the process used to complete them. INSTRUCTIONS: Graph each sstem of linear inequalities. {(, ) 1,!,!} 1) {(, ) 3,!,!} 1a: Graph the first inequalit. 1b: Graph the second inequalit intercept = b = 1 This inequalit has a horizontal boundar slope = m = 1 passing through the -ais at = variables is/are anthing other than real numbers. Because the MATHEMATICAL restrictions are real numbers!,! the overlapping area is not stippled. The solution to the sstem is the graph created in step 1 (shown above).

2 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES ) {(, ) >, I, I} {(, ) <5, I, I} 1a: Graph the first inequalit. 1b: Graph the second inequalit. > >1 + 0 <5 -intercept = b = 0 slope = m = 1 1 This inequalit has a horizontal boundar passing through the -ais at = variables is/are anthing other than real numbers. Because the MATHEMATICAL restrictions are Integers I, I the overlapping area is stippled

3 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 3 3) {( P, M) M < 3, P W, M W} {( P, M) M 3P, P W, M W} 1a: Graph the first inequalit. 1b: Graph the second inequalit. M < 3 M 3P This inequalit has a horizontal boundar M-intercept = b = passing through the M-ais at = 3 slope = m = variables is/are anthing other than real numbers. Because the MATHEMATICAL restrictions are Whole numbers, W, W, the points in the overlapping shaded area that have non-negative entire number coordinates are stippled as shown

4 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES ) {(, ) 3 7 5, I, I} {(, ) , N, N} 1a: Graph the first inequalit. 1b: Graph the second inequalit. Because the -intercepts are fractions, not entire numbers, calculate the -intercepts for each inequalit then graph them using the & -intercepts. Because ou are calculating specific points on the grid, change the inequalit signs to a = signs.

5 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 5 Continued on the net page. variables is/are anthing other than real numbers. Because the most restrictive MATHEMATICAL restriction is Whole numbers, W, the points in the overlapping shaded area that have non-negative entire number coordinates are stippled as shown. 5) {(, ) 7 +00,!,!} {(, ) 5 } ,!,! 1a: Graph the first inequalit. 1b: Graph the second inequalit intercept = b = 00 -intercept = b = 00 slope = m = 7 slope = m = 5 7 Because the -intercepts are ver large, calculate the -intercepts for each inequalit then graph them using the & -intercepts. Because ou are calculating specific points on the grid, change the inequalit signs to a = signs. Continued on the net page.

6 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES variables is/are anthing other than real numbers. Because the most restrictive MATHEMATICAL restrictions is Natural numbers,!, the points in the overlapping shaded area that have positive entire number coordinates are stippled as shown. C) REQUIRED PRACTICE 1: Complete these problems in the order listed. SHOW THE PROCESS!! 1) Page 307: Question. {Ans. Page 557} ) Page : Questions 1,,, 7, 9, 3 & 1. {Ans. Page 55-50}

7 FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 7 ASSIGNMENT: PRINT THIS INFORMATION ON YOUR OWN GRID PAPER LAST then FIRST Name T1 SYSTEMS OF LINEAR INEQUALITIES Block: Show the process required to complete each problem to avoid receiving a zero grade. Neatness Counts!!! (Marks indicated in italicized brackets.) REMEMBER TO USE GRID PAPER FOR ALL ASSIGNMENTS!!! GRAPH EACH INEQUALITY ON ITS OWN GRID!!! Show the process required to complete each problem to avoid receiving a zero grade. Neatness Counts!!! (Marks indicated in italicized brackets.) REMEMBER TO USE GRID PAPER FOR ALL ASSIGNMENTS!!! Graph these sstems of inequalities. BE SURE YOU INCLUDE ALL RELEVENT INORMATION. 1) {(, ),!,!} {(, ) >,!,!} (5) ) {(, ) + >, W, W} {(, ) +, W, W} (9) 3) {(, ) 5 0,!,!} {(, ) ,!,!} (15) Following the instructions. (1) /30