Substitute –2 and –1 for r and s in the first equation and solve for t. 3-4 Systems of Equations in Three Variables Solve each system of equations. 11. Therefore, the solution is (–2, –1, 4). SOLUTION: 12. SOLUTION: Eliminate one variable. Multiply the first equation by –4 and add with the second equation. Eliminate one variable. Multiply the first equation by 2 and add with the second equation. Multiply the third equation by 2, and add with the second equation. Multiply the second equation by 2 and the third equation by 4 then add. Solve the fourth and fifth equations . Solve the fourth and the fifth equation. Substitute –2 for r in the fifth equation and solve for s. This is a false statement. Therefore, there is no solution. 13. Substitute –2 and –1 for r and s in the first equation and solve for t. SOLUTION: eSolutions Manual - Powered by Cognero Therefore, the solution is (–2, –1, 4). Page 1 Eliminate one variable. This is a of false statement.inTherefore, there is no 3-4 Systems Equations Three Variables solution. Eliminate one variable. Multiply the second equation by –3 and add with the first equation. 13. SOLUTION: Multiply the second and third equation by 5 and –2 respectively and add. Eliminate one variable. Add the first and the third equations. Solve the fourth and fifth equations. Multiply the first equation by 3 and add with the second equation. Substitute 3 for y in the fourth equation and solve for x. Multiply the third equation by –3 and add with the second equation. Substitute –1 and 3 for x and y in the first equation and solve for z. Since the equations 4, 5 and 6 are same, the system has an infinite number of solutions. 14. Therefore, the solution is (–1, 3, 7). SOLUTION: Eliminate one variable. Multiply the second equation by –3 and add with the first equation. eSolutions Manual - Powered by Cognero 21. AMUSEMENT PARKS Nick goes to the amusement park to ride roller coasters, bumper cars, and water slides. The wait for the roller coasters is 1 hour, the wait for the bumper cars is 20 minutes long, and the wait for the water slides is only 15 minutes long. Nick rode 10 total rides during his visit. Because he enjoys roller coasters the most, the number of times he rode the roller coasters was the sum of the times he rode the other two rides. If Nick waited in line for a total of 6 hours and 20 minutes, how many of each ride did he go on? Page 2 SOLUTION: Let x, y and z be the number of raids in roller and the wait for the water slides is only 15 minutes long. Nick rode 10 total rides during his visit. Because he enjoys roller coasters the most, the number of he rodeinthe rollerVariables coasters was the 3-4 Systems oftimes Equations Three sum of the times he rode the other two rides. If Nick waited in line for a total of 6 hours and 20 minutes, how many of each ride did he go on? SOLUTION: Let x, y and z be the number of raids in roller coaster, bumper car and water slide respectively. Nick rode 10 rides during his visit. The number of times that Nick rode the roller coaster is the sum of the times he rode the other two rides. So: Substitute 1 for y in the fifth equation and solve for z. Nick rode the roller coaster, bumper cars and water slides 5, 1 and 4 times respectively. 23. FINANCIAL LITERACY Kate invested $100,000 in three different accounts. If she invested $30,000 more in account A than account C and is expected to earn $6300 in interest, how much did she invest in each account? He waited in line for a total of 6 hours 20 minutes. Substitute x for y + z in the first equation and solve for x. SOLUTION: Let a, b and c be the amount invested in the Account A, B and C respectively. Kate invested $30,000 more in account A than account C. Substitute 5 for x in the second and the third equation and simplify. Therefore, Substitute c + 30000 for a in the first equation and simplify. Total interest amount is $6300. That is, Multiply the fifth equation by –3 and add with the fourth equation. . Substitute c + 30000 for a and simplify. Substitute 1 for y in the fifth equation and solve for z. Solve the third and fourth equations. eSolutions Manual - Powered by Cognero Nick rode the roller coaster, bumper cars and water Page 3 3-4 Systems of Equations in Three Variables Solve the third and fourth equations. –10), (–5, –101), and (6, –90), determine the values of a, b, and c and write the general form of the equation. SOLUTION: Substitute the points (2, –10), (–5, –101), and (6, – 90) in the equation . Substitute 25000 for c in the second equation and solve for a. Substitute 25000 for c in the third equation and solve for b. Solve the equations 1, 2 and 3. Solve the fourth and fifth equations. Therefore, she invested $55,000, $20,000 and $25,000 in the account A, B and C respectively. 24. CCSS REASONING Write a system of equations to represent the three rows of figures below. Use the system to find the number of red triangles that will balance one green circle. Substitute –3 for a in the fourth equation and solve for b. SOLUTION: t + c = s, p + t = c, 2s = 3p where t represents triangle, c represents circle, s represents square, and p represents pentagon; 5 red triangles 25. CHALLENGE The general form of an equation for a parabola is where (x, y) is a point on the parabola. If three points on a parabola are (2, –10), (–5, –101), and (6, –90), determine the values of a, b, and c and write the general form of the equation. SOLUTION: Substitute the points (2, –10), (–5, –101), and (6, – 90) in the equation eSolutions Manual - Powered by Cognero Substitute –3 and 4 for a and b in the first equation. The value of a, b and c are –3, 4 and –6 respectively. 2 Therefore, the equation of the parabola is y = –3x + 4x – 6. 30. What is the solution of the system of equations shown below? . Page 4 A (0, 3, 3) respectively. 2 Therefore, the equation of the parabola is y = –3x + 4x – 6. 3-4 Systems of Equations in Three Variables 30. What is the solution of the system of equations shown below? Substitute 2 and 5 for x and y in the first equation and solve for z. A (0, 3, 3) B (2, 5, 3) C no solution D infinitely many solutions The solution is (2, 5, 3). Option B is the correct answer. 31. ACT/SAT The graph shows which system of equations? SOLUTION: Eliminate one variable. Multiply the first equation by 2 and with the second equation. A D B E Multiply the second equation by 2 and add with the third equation. Solve the fourth and fifth equations. C Substitute 2 for x in the fourth equation and solve for y. SOLUTION: The lines intersect at (3, –2). Substitute the point in each system of equations. Substitute 2 and 5 for x and y in the first equation and solve for z. eSolutions Manual - Powered by Cognero Page 5 3-4 Systems of Equations in Three Variables First system of equations satisfies the point (3, –2). Therefore, option A is the correct answer. eSolutions Manual - Powered by Cognero Page 6
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