Solve the system of equations by any method. 3x – 4y + 2z = -17 (1) 2x + 4y + z = 21 (2) 2x + 3y + 5z = 28 (3) Enter the exact answer as an ordered triple, (x, Y, z). Hint: There are multiple ways to solve this system of equations. • strategy is to eliminate one of the variables and end up with 2 equations in 2 variables. • One way to do that is to begin with equation 2 to get z = 21 – 2 1 – 4 y. • Then substitute 21 – 2 x – 4 y for z in equations 1 and 3. • You now have 2 equations (the modified equations 1 and 3) in 2 variables (x and y). • Solve this smaller system for a and y and then use z = 21 – 2 x – 4 y to calculate z.
Solve the system of equations by any method. 3x – 4y + 2z = -17 (1) 2x + 4y + z = 21 (2) 2x + 3y + 5z = 28 (3) Enter the exact answer as an ordered triple, (x, Y, z). Hint: There are multiple ways to solve this system of equations. • strategy is to eliminate one of the variables and end up with 2 equations in 2 variables. • One way to do that is to begin with equation 2 to get z = 21 – 2 1 – 4 y. • Then substitute 21 – 2 x – 4 y for z in equations 1 and 3. • You now have 2 equations (the modified equations 1 and 3) in 2 variables (x and y). • Solve this smaller system for a and y and then use z = 21 – 2 x – 4 y to calculate z.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.7: Puzzle Problems
Problem 33P
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Transcribed Image Text:Solve the system of equations by any method.
3x – 4y + 2z =-17
(1)
2x + 4y + z = 21
(2)
2x + 3y + 5z = 28
(3)
Enter the exact answer as an ordered triple, (x, y, z).
Hint: There are multiple ways to solve this system of equations.
• Astrategy is to eliminate one of the variables and end up with 2 equations in 2 variables.
• One way to do that is to begin with equation 2 to get z= 21 – 2 x – 4 y.
• Then substitute 21 – 2 x – 4 y for z in equations 1 and 3.
• You now have 2 equations (the modified equations 1 and 3) in 2 variables (x and y).
• Solve this smaller system for æ and y and then use z= 21 – 2 x – 4 y to calculate z.
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