Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Solving Systems Using Solve each equation.Substitution ALGEBRA 1 LESSON 9-2 (For help, go to Lessons2-4 and 7-1.) 1. m – 6 = 4m + 8 2. 4n = 9 – 2n 3. 1 t + 5 = 10 3 For each system, is the ordered pair a solution of both equations? 4. (5, 1) y = –x + 4 5. (2, 2.4) 4x + 5y = 20 y=x–6 2x + 6y = 10 9-2 Solving Systems Using Substitution ALGEBRA 1 LESSON 9-2 Solutions 1. m – 6 = 4m + 8 m – m – 6 = 4m – m + 8 –6 = 3m + 8 2. n = 11 –14 = 3m –4 2 = m 2 3 3. 4n = 9 – 2n 4n + 2n = 9 – 2n + 2n 6n = 9 1 t + 5 = 10 3 1t =5 3 t = 15 9-2 Solving Systems Using Substitution Solutions (continued) ALGEBRA 1 LESSON 9-2 4. (5, 1) in y = –x + 4 1 –5 + 4 1 =/ –1 (5, 1) in y = x – 6 1 5–6 1 =/ –1 no no No, (5, 1) is not a solution of both equations. 5. (2, 2.4) in 4x + 5y = 20 4(2) + 5(2.4) 20 (2, 2.4) in 2x + 6y = 10 2(2) + 6(2.4) 10 8 + 12 20 20 = 20 yes 4 + 14.4 10 18.4 =/ 10 no No, (2, 2.4) is not a solution of both equations. 9-2 Solving Systems Using Substitution Solve using substitution. y = 2x + 2 ALGEBRA 1 LESSON 9-2 y = –3x + 4 Step 1: Write an equation containing only one variable and solve. y = 2x + 2 –3x + 4 = 2x + 2 4 = 5x + 2 2 = 5x 0.4 = x Start with one equation. Substitute –3x + 4 for y in that equation. Add 3x to each side. Subtract 2 from each side. Divide each side by 5. Step 2: Solve for the other variable. y = 2(0.4) + 2 y = 0.8 + 2 y = 2.8 Substitute 0.4 for x in either equation. Simplify. 9-2 Solving Systems Using Substitution ALGEBRA 1 LESSON 9-2 (continued) Since x = 0.4 and y = 2.8, the solution is (0.4, 2.8). Check: See if (0.4, 2.8) satisfies y = –3x + 4 since y = 2x + 2 was used in Step 2. 2.8 –3(0.4) + 4 2.8 –1.2 + 4 2.8 = 2.8 Substitute (0.4, 2.8) for (x, y) in the equation. 9-2 Solving Systems Using Substitution Solve using substitution. ALGEBRA 1 LESSON 9-2 –2x + y = –1 4x + 2y = 12 Step 1: Solve the first equation for y because it has a coefficient of 1. –2x + y = –1 y = 2x –1 Add 2x to each side. Step 2: Write an equation containing only one variable and solve. 4x + 2y = 12 4x + 2(2x –1) = 12 4x + 4x –2 = 12 8x = 14 x = 1.75 Start with the other equation. Substitute 2x –1 for y in that equation. Use the Distributive Property. Combine like terms and add 2 to each side. Divide each side by 8. 9-2 Solving Systems Using Substitution ALGEBRA 1 LESSON 9-2 (continued) Step 3: Solve for y in the other equation. –2(1.75) + y = 1 –3.5 + y = –1 y = 2.5 Substitute 1.75 for x. Simplify. Add 3.5 to each side. Since x = 1.75 and y = 2.5, the solution is (1.75, 2.5). 9-2 Solving Systems Using Substitution A youth group with 26 members is going to the beach. There ALGEBRA 1 LESSON 9-2 will also be five chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed? Let v = number of vans and c = number of cars. Drivers Persons v 7 v + + c 5 c = 5 = 31 Solve using substitution. Step 1: Write an equation containing only one variable. v+c=5 Solve the first equation for c. c = –v + 5 9-2 Solving Systems Using Substitution ALGEBRA 1 LESSON 9-2 (continued) Step 2: Write and solve an equation containing the variable v. 7v + 5c = 31 7v + 5(–v + 5) = 31 7v – 5v + 25 = 31 2v + 25 = 31 2v = 6 v =3 Substitute –v + 5 for c in the second equation. Solve for v. Step 3: Solve for c in either equation. 3+c=5 c=2 Substitute 3 for v in the first equation. 9-2 Solving Systems Using Substitution ALGEBRA 1 LESSON 9-2 (continued) Three vans and two cars are needed to transport 31 persons. Check: Is the answer reasonable? Three vans each transporting 7 persons is 3(7), of 21 persons. Two cars each transporting 5 persons is 2(5), or 10 persons. The total number of persons transported by vans and cars is 21 + 10, or 31. The answer is correct. 9-2 Solving Systems Using Substitution Solve each system using substitution. ALGEBRA 1 LESSON 9-2 1. 5x + 4y = 5 2. 3x + y = 4 3. 6m – 2n = 7 y = 5x 2x – y = 6 3m + n = 4 (0.2, 1) (2, 2) (1.25, 0.25) 9-2