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Solve the system of linear equations and check any solution algebraically. 5x + 4y + 14z = 0 6x + 5y + 19z = 0 5x + 3y + 16z = 0

Solve the system of linear equations and check any solution algebraically. 5x + 4y + 14z = 0 6x + 5y + 19z = 0 5x + 3y + 16z = 0

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter5: Solving Systems Of Linear Equations
Section: Chapter Questions
Problem 2CR
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Solve the system of linear equations and check any solution algebraically. 5x + 4y + 14z = 0 6x + 5y + 19z = 0 5x + 3y + 16z =
Transcribed Image Text:Solve the system of linear equations and check any solution algebraically. 5x + 4y + 14z = 0 6x + 5y + 19z = 0 5x + 3y + 16z =
The solution is the ordered triple (x, y, z) that satisfies all three equations. Convert the system to an equivalent system that is in the row echelon form, by using row operations. In the row echelon form, the equations have a stair-step pattern with leading coefficients of 1. Write the system with the first two equations interchanged. ]× )v + (D |× )z = 0 Equation 1 + = 0 Equation 2 = 0 Equation 3 5x 4y 14z 5x 3y 16z Multiply Equation 2 by (-1) and add with Equation 1 to make the leading coefficient in the first row 1. |× )x + 5y + ]× )v ]× ) . 6х + + 19z + = 0 + + Eq 1 + (-1)Eq 2 + Eq 2 + Eq 3 5x 4y 14z = 0 5x 3y + 16z = 0 Write the equivalent system with the resultant Equation 1. |× )z x + y + = 0 + Eq 1 = 0 + Eq 2 = 0 + Eq 3 5х + 4y + 14z 5x + 3у + 16z
Transcribed Image Text:The solution is the ordered triple (x, y, z) that satisfies all three equations. Convert the system to an equivalent system that is in the row echelon form, by using row operations. In the row echelon form, the equations have a stair-step pattern with leading coefficients of 1. Write the system with the first two equations interchanged. ]× )v + (D |× )z = 0 Equation 1 + = 0 Equation 2 = 0 Equation 3 5x 4y 14z 5x 3y 16z Multiply Equation 2 by (-1) and add with Equation 1 to make the leading coefficient in the first row 1. |× )x + 5y + ]× )v ]× ) . 6х + + 19z + = 0 + + Eq 1 + (-1)Eq 2 + Eq 2 + Eq 3 5x 4y 14z = 0 5x 3y + 16z = 0 Write the equivalent system with the resultant Equation 1. |× )z x + y + = 0 + Eq 1 = 0 + Eq 2 = 0 + Eq 3 5х + 4y + 14z 5x + 3у + 16z
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