Name: lass: ate: I: U2Q5 (Module 7 Practice Quiz) Multiple hoice Identify the choice that best completes the statement or answers the question. Ï y = x + 8 1. Solve Ô Ì. ÓÔ x + y = 7 a. This system has infinitely many solutions. b. This system has no solutions. c. ( 1, 15 2 2 d. ( 1 2, 17 2 ) Ï y = 2x 1 2. Solve Ô Ì. ÓÔ 2x y 1 = 0 a. This system has infinitely many solutions. b. This system has exactly one solution. c. This system has no solution. d. (1, 1) and (0, 0) Ï x 8y = 6 3. lassify Ô Ì. Give the number of solutions. ÓÔ 2x 16y = 12 a. This system is consistent. It has infinitely many solutions. b. This system is inconsistent. It has infinitely many solutions. c. This system is inconsistent. It has no solutions. d. This system is consistent. It has one solution. 4. Elena and her husband Marc both drive to work. Elena s car has a current mileage (total distance driven) of 9,000 and she drives 18,000 miles more each year. Marc s car has a current mileage of 60,000 and he drives 7,000 miles more each year. Will the mileages for the two cars ever be equal? Explain. a. No; The equations have equal slopes but different y-intercepts, so the lines do not intersect b. No; The equations have different slopes, so the lines do not intersect. c. Yes; The equations have different slopes, so the lines intersect. d. Yes; The equations have different y-intercepts, so the lines intersect. Ï 6x 7y = 18 5. lassify Ô Ì. ÓÔ 14y 12x = 36 a. onsistent and dependent system b. Inconsistent and independent system c. Inconsistent and dependent system d. onsistent and independent system 6. Tell whether (8, 5) is a solution of y > x + 7. a. Yes, (8, 5) is a solution of y > x + 7. b. No, (8, 5) is not a solution of y > x + 7. 1
Name: I: 7. Tell whether (9, 2) is a solution of y < 4x + 1. a. Yes, (9, 2) is a solution of y < 4x + 1. b. No, (9, 2) is not a solution of y < 4x + 1. 8. Graph the solutions of the linear inequality 8x + 2y > 6. a. c. b. d. 2
Name: I: 9. Tony has $18 to buy apples and bananas for a fruit salad. pples cost $2 per pound and bananas cost $1 per pound. Write and graph an inequality to describe the situation. Then give two possible combinations of pounds of apples and bananas that Tony can buy. 3
Name: I: a. 2a + b 18; 2 pounds of apples and 12 pounds of bananas or 4 pounds of apples and 2 pounds of bananas. b. 2a + b 18; 2 pounds of apples and 12 pounds of bananas or 4 pounds of apples and 2 pounds of bananas. c. 2a + b 18; 2 pounds of apples and 18 pounds of bananas or 4 pounds of apples and 16 pounds of bananas. 4
Name: I: d. 2a + b 18; 2 pounds of apples and 18 pounds of bananas or 4 pounds of apples and 16 pounds of bananas. 10. Write an inequality to represent the graph. a. y > 2x + 3 c. y < 3x + 2 b. y 2x + 3 d. y < 2x + 3 5
Name: I: 11. Graph the inequality 0 > 9 + 6x 9y. a. c. b. d. Ï y 4x 12. Tell whether (2, 7) is a solution of Ô Ì. ÓÔ y < x + 2 a. No, (2, 7) is not a solution of the system. b. Yes, (2, 7) is a solution of the system. 6
Name: I: Ï y < 3x + 2 13. Graph the system of linear inequalities Ô Ì. Give two ordered pairs that are solutions and two that ÓÔ y 4x 1 are not solutions. a. (0, 0) and ( 4, 5) are solutions. (2, 2) and (10, 1) are not solutions. c. (2, 2) and (0, 10) are solutions. (0, 0) and ( 5, 1) are not solutions. b. (1, 2) and ( 6, 0) are solutions. (1, 5) and (0, 0) are not solutions. d. (5, 6) and (0, 0) are solutions. (1, 1) and (2, 0) are not solutions. 7
Name: I: Ï y 2x + 4 14. Graph the system of linear inequalities Ô Ì. ÓÔ y 2x 2 a. c. b. d. 15. Estimate the area of the overlapping solution regions. Ï x 0 Ô Ì y x 2.5 ÓÔ y x + 4 a. bout 12 square units c. bout 10 square units b. bout 19 square units d. bout 8 square units 8
I: U2Q5 (Module 7 Practice Quiz) nswer Section MULTIPLE HOIE 1. NS: Write each equation in slope-intercept form. y = x + 8 y = x + 7 The lines both have slope 1 but different y-intercepts, so they are parallel. Parallel lines never intersect so the system has no solutions and is inconsistent. Write both equations in slope-intercept form to see if the lines are parallel or the same line. Only lines with the same graph have infinitely many solutions. Write both equations in slope-intercept form to see if the lines are parallel. Write both equations in slope-intercept form to see if the lines are parallel. PTS: 1 IF: 2 REF: 1135d19a-4683-11df-9c7d-001185f0d2ea OJ: 7-1.1 Systems with No Solution NT: NT.SS.MTH.10.9-12..REI.6 ST: M9-12..REI.6 LO: MTH..10.09.01.01.02.01.001 TOP: 7-1 Solving Special Systems KEY: system of equations special systems no solution OK: OK 2 1
I: 2. NS: Method 1 ompare slopes and y-intercepts. y = 2x 1 y = 2x 1 Write both equations in slope-intercept form. The lines 2x y 1 = 0 y = 2x 1 have the same slope and the same y-intercept. There are infinitely many solutions. The graph of this system of equations would be the same line. Method 2 Solve the system algebraically. Use the elimination method. y = 2x 1 Write equations to line up like terms. 2x + y = 1 2x y 1 = 0 dd the equations. 2x y = 1 0 = 0 The equation is an identity. There are infinitely many solutions. ompare the slopes and y-intercepts. The graph of the system will be the same line. The graph of the system will be the same line. PTS: 1 IF: 2 REF: 113833f6-4683-11df-9c7d-001185f0d2ea OJ: 7-1.2 Systems with Infinitely Many Solutions NT: NT.SS.MTH.10.9-12..REI.6 ST: M9-12..REI.6 LO: MTH..10.09.01.01.02.02.001 TOP: 7-1 Solving Special Systems KEY: system of equations infinitely many solutions identity OK: OK 2 3. NS: Write both equations in slope-intercept form. y = 1 8 x 3 4 y = 1 8 x 3 4 These are the same line because they have the same slope and the same y-intercept. First, write both equations in slope-intercept form. Then, compare the slopes and y-intercepts. First, write both equations in slope-intercept form. Then, compare the slopes and y-intercepts. First, write both equations in slope-intercept form. Then, compare the slopes and y-intercepts. PTS: 1 IF: 1 REF: 11385b06-4683-11df-9c7d-001185f0d2ea OJ: 7-1.3 lassifying Systems of Linear Equations ST: M9-12..REI.6 LO: MTH..10.09.01.01.02.02.001 TOP: 7-1 Solving Special Systems KEY: classifying systems consistent inconsistent OK: OK 2 2
I: 4. NS: Write a system of equations. Total mileage is miles per year plus current mileage Elena y = 18,000 n + 9,000 Marc y = 7,000 n + 60,000 If the slopes of the lines are different, then the lines intersect and the mileages will be equal for some value of n. The slope of the line for Elena s mileage is 18,000 and the slope of the line for Marc s mileage is 7,000. Therefore, the lines intersect, and the mileages will be equal. Write a linear equation to model the mileage of each car. The distances driven each year are the slopes in the equations. Write a linear equation to model the mileage of each car. If the slopes of the lines are different, the lines intersect. Write a linear equation to model the mileage of each car. If the slopes of the lines are different, the lines intersect. PTS: 1 IF: 2 REF: 113a9652-4683-11df-9c7d-001185f0d2ea OJ: 7-1.4 pplication ST: M9-12..REI.6 M9-12..E.2 LO: MTH..10.09.01.01.006 TOP: 7-1 Solving Special Systems KEY: solving system of equations rate OK: OK 2 5. NS: Multiplying the first equation by 2 creates the second equation. The lines are the same because the equations have the same slope and the same y-intercept. Therefore, the system is consistent and dependent. The system has infinitely many solutions. n inconsistent system has no solutions, which means the lines are parallel. n inconsistent system has no solutions, which means the lines are parallel. n independent system has exactly one solution, which means the graph of the system consists of two intersecting lines. PTS: 1 IF: 3 REF: 113abd62-4683-11df-9c7d-001185f0d2ea ST: M9-12..REI.6 LO: MTH..10.09.01.01.02.02.001 MTH..10.09.01.01.02.02.003 TOP: 7-1 Solving Special Systems KEY: system of equations classify consistent dependent OK: OK 2 3
I: 6. NS: Substitute (8, 5) for (x, y) in y > x + 7. y > x + 7 5 > (8) + 7 5 > 15, false (8, 5) is not a solution of y > x + 7. Substitute the values for (x, y) into the inequality to see if the ordered pair is a solution. PTS: 1 IF: 1 REF: 113cf8ae-4683-11df-9c7d-001185f0d2ea OJ: 7-2.1 Identifying Solutions of Inequalities ST: M9-12..REI.12 TOP: 7-2 Solving Linear Inequalities KEY: inequalities linear OK: OK 2 7. NS: Substitute (9, 2) for (x, y) in y < 4x + 1. y < 4x + 1 2 < 4(9) + 1 2 < 37, true (9, 2) is a solution of y < 4x + 1. Substitute the values for (x, y) into the inequality to see if the ordered pair is a solution. PTS: 1 IF: 1 REF: 113f5b0a-4683-11df-9c7d-001185f0d2ea OJ: 7-2.1 Identifying Solutions of Inequalities ST: M9-12..REI.12 TOP: 7-2 Solving Linear Inequalities KEY: inequalities linear OK: OK 2 4
I: 8. NS: Step 1. Solve the inequality 8x + 2y > 6 for y. y > 4x 3 Step 2. Graph the boundary line y = 4x 3. Use a dashed line for >. Step 3. The inequality is >, so shade above the line. heck the boundary and the shading. The shaded region includes points that make the inequality true. The line is solid only when the operator is not > or <. PTS: 1 IF: 2 REF: 113f821a-4683-11df-9c7d-001185f0d2ea OJ: 7-2.2 Graphing Linear Inequalities in Two Variables NT: NT.SS.MTH.10.9-12..REI.12 ST: M9-12..REI.12 LO: MTH..10.09.01.02.005 TOP: 7-2 Solving Linear Inequalities KEY: inequalities linear OK: OK 2 9. NS: Let b be the number of pounds of bananas and a be the number of pounds of apples. The inequality is 2a + b 18. Solving for b gives b 2a + 18. Graph the line b = 2a + 18. The inequality is, so shade below the line. To find a point that satisfies the inequality, select a value for a. Then look on the graph for a point with that a-value that lies in the shaded region. heck the inequality symbol. Shade on the correct side of the line. Tony must spend no more than the given amount of money. heck the inequality symbol. PTS: 1 IF: 2 REF: 1141bd66-4683-11df-9c7d-001185f0d2ea OJ: 7-2.3 pplication NT: NT.SS.MTH.10.9-12..REI.12 NT.SS.MTH.10.9-12..E.3 ST: M9-12..REI.12 M9-12..E.3 LO: MTH..10.09.01.02.005 MTH..10.09.01.02.006 TOP: 7-2 Solving Linear Inequalities KEY: coordinate plane graph linear inequality solutions multi-step OK: OK 3 5
I: 10. NS: Use the graph to determine the slope and y-intercept, and then write an equation in the form y = mx + b. graph shaded above the line means greater than and the graph shaded below the line means less than. Use or if the line is solid; use < or > if the line is dashed. heck the direction of the inequality symbol. Use "greater than or equal to" or "less than or equal to" for a solid line. Use "greater than" or "less than" for a dashed line. Use the graph to find the slope and y-intercept. Then write an equation for the boundary line in the form y = mx + b, where m is the slope and b is the y-intercept. PTS: 1 IF: 2 REF: 11441fc2-4683-11df-9c7d-001185f0d2ea OJ: 7-2.4 Writing an Inequality from a Graph ST: M9-12..REI.12 LO: MTH..10.09.01.02.007 TOP: 7-2 Solving Linear Inequalities KEY: graph inequality equation of a line OK: OK 2 6
I: 11. NS: 0 > 9 + 6x 9y 0 > 3 + 2x 3y ivide the equation by a common factor, 3. 3y > 2x + 3 dd 3y to both sides. y > 2 3 x 3 3 ivide both sides by 3. Write the equation in slope-intercept form. m = 2 3 and b = 3 3 = 1 Graph the boundary line. Use a solid line for or. Use a dashed line for < or >. Shade the half-plane above the line if y > or y. Shade the half-plane below the line if y < or y. First, solve the inequality for y. Then, graph the boundary line and shade above or below the line. When graphing inequalities, graph the boundary line, and then plug in (0,0) to see which side to shade. When graphing inequalities, graph the boundary line, and then plug in (0,0) to see which side to shade. PTS: 1 IF: 3 REF: 114446d2-4683-11df-9c7d-001185f0d2ea NT: NT.SS.MTH.10.9-12..REI.12 ST: M9-12..REI.12 LO: MTH..10.09.01.02.005 TOP: 7-2 Solving Linear Inequalities KEY: inequalities linear graph OK: OK 3 7
I: 12. NS: heck by substituting the coordinates into both inequalities. If (2, 7) satisfies both inequalities, then it is a solution of the system. y 4x y < x + 2 7 4( 2) 7 < 2 + 2 7 8 FLSE 7 < 4 FLSE heck to see whether the ordered pair satisfies both inequalities. If it does, it is a solution. PTS: 1 IF: 1 REF: 1146821e-4683-11df-9c7d-001185f0d2ea OJ: 7-3.1 Identifying Solutions of Systems of Linear Inequalities ST: M9-12..REI.12 TOP: 7-3 Solving Systems of Linear Inequalities KEY: inequalities system linear OK: OK 2 13. NS: Graph y < 3x + 2 and y 4x 1 on the same coordinate plane. The solutions of the system are the overlapping shaded regions, including the solid boundary line. The solutions are the overlapping shaded regions. heck the inequality symbols before graphing. The solutions are the overlapping shaded regions. PTS: 1 IF: 2 REF: 1148e47a-4683-11df-9c7d-001185f0d2ea OJ: 7-3.2 Solving a System of Linear Inequalities by Graphing NT: NT.SS.MTH.10.9-12..REI.12 NT.SS.MTH.10.9-12..E.3 ST: M9-12..REI.12 M9-12..E.3 LO: MTH..10.09.01.02.005 TOP: 7-3 Solving Systems of Linear Inequalities KEY: inequalities system linear OK: OK 3 8
I: 14. NS: Graph the first linear inequality. Since the symbol is ³, draw a solid boundary line and shade the upper half region. Now graph the second linear inequality. Since the symbol is, draw a solid boundary line and shade the lower half region. Test a point on one side of each boundary line before deciding where to shade. Test a point on one side of the first boundary line before deciding where to shade. Test a point on one side of the second boundary line before deciding where to shade. PTS: 1 IF: 2 REF: 11490b8a-4683-11df-9c7d-001185f0d2ea OJ: 7-3.3 Graphing Systems with Parallel oundary Lines NT: NT.SS.MTH.10.9-12..REI.12 ST: M9-12..REI.12 LO: MTH..10.09.01.02.005 TOP: 7-3 Solving Systems of Linear Inequalities KEY: inequalities system linear OK: OK 2 9
I: 15. NS: Graph the system of inequalities. The overlapping solution regions form a triangle. The height of the triangle is about 3 units, and the base of the triangle is about 6.5 units. rea = 1 (base)(height) 1 (6.5)(3) 10 square units 2 2 First, graph the system of inequalities and find the shape formed by their overlapping regions. Then, estimate the area of this shape by using its dimensions. The graph of the system of inequalities should be a triangle. Use the dimensions of the triangle to estimate the area. First, graph the system of inequalities and find the shape formed by their overlapping regions. Then, estimate the area of this shape by using its dimensions. PTS: 1 IF: 3 REF: 114da932-4683-11df-9c7d-001185f0d2ea ST: M9-12..REI.12 LO: MTH..10.09.01.02.005 TOP: 7-3 Solving Systems of Linear Inequalities KEY: inequalities system linear solution region OK: OK 4 10