To determine To calculate: The solution of the system of equation 5 x − 6 z = − 17 , 3 x − 4 y + 5 z = − 20 , 2 z = − 6 by substitution method. Explanation Given Information: The provided system of equation is 5 x − 6 z = − 17 , 3 x − 4 y + 5 z = − 20 , 2 z = − 6 . Formula used: Steps for substitution method: Step 1) Find a variable with coefficient 1 and solve the equation for the corresponding variable. If there is no variable with coefficient 1 , solve for any variable in any equation. Step 2) Substitute the value of the variable obtained in the step 1 into the other equations and simplify the equation to eliminate one variable from the equations. Step 3) Find the value of the variables by solving the equations obtained in step 2 . Step 4) Substitute the value of the variables obtained in step 3 in the equation obtained in step 1 . Step 5) Now, write the solution as an ordered triple. Step 6) Verify your solution, by substituting the value in all the equations. Calculation: Consider the system of equations 5 x − 6 z = − 17 , 3 x − 4 y + 5 z = − 20 , 2 z = − 6 . Observe that the equation 2 z = − 6 contains only one variable, hence solve it to determine the value of variable. 2 z = − 6 z = − 6 2 z = − 3 Substitute z = − 3 in the equation 5 x − 6 z = − 17 and solve to obtain the value of x . 5 x − 6 z = − 17 5 x − 6 ⋅ ( − 3 ) = − 17 5 x + 18 = − 17 5 x = − 17 − 18 Solve further, 5 x = − 17 − 18 x = − 35 5 x = − 7 Substitute x = − 7 and z = − 3 in the equation 5 x − 6 z = − 17 , 3 x − 4 y + 5 z = − 20 , 2 z = − 6 . 3 ⋅ ( − 7 ) − 4 y + 5 ⋅ ( − 3 ) = − 20 − 21 − 4 y − 15 = − 20 − 4 y = − 20 + 21 + 15 − 4 y = 16 Solve further, − 4 y = 16 y = 16 − 4 y = − 4 The solution of the system of equations x + 2 y = 6 , 3 y = 9 , x + 2 z = 12 is ( − 7 , − 4 , − 3 )

Intermediate Algebra For College Students (10th Edition)

10th Edition

ISBN: 9780134758992

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.2, Problem 6ES

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To calculate: The solution of the system of equation 5x−6z=−17, 3x−4y+5z=−20, 2z=−6 by substitution method.

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Chapter 4.2, Problem 5ES

Chapter 4.2, Problem 7ES

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