9th Edition

ISBN: 9780321716835

Author: Michael Sullivan

Publisher: Addison Wesley

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Question

Chapter 11, Problem 18RE

To determine

Solve each system of equations using the method of substitution ot the method of elimination.

Expert Solution & Answer

Answer to Problem 18RE

It is inconsistent.

Explanation of Solution

Given information:

Solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

${x−4y+3z=15−3x+y−5z=−5−7x−5y−9z=10$

Calculation:

The given system of equations in three variables is given by the expressions given below.

${x−4y+3z=15−3x+y−5z=−5−7x−5y−9z=10$

The given system consists of three variables from which one of the variables is required to be removed from the equations. This can be done by multiplying first equations by $15$ and the second equation by $−9$ and the third equation by $−5$ . The equations obtained are given below.

${15x−60y+45=22527x−9y+45z=4535x+25y+45z=−50$

We can now obtain two equations in $x$ and $y$ which can be solved simultaneously by subtracting

Second equation from the first equation and by subtracting third equation from the first equation.

${27x−15x−9y−(−60y)+45z−45z−22535x−15x+25y−(−60y)+45z−45z=−50−225$

${12x+51y=−18020x+85y=−275$

The given system of equations can be solved by the method of elimination. The first equation can be multiplied by $5$ and second equation can be multiplied by $3$ in order make the coefficient of $x$ same in both the equations.

${12x+51y=−180)×5(20x+85y=−275)×3$

${60x+255y=−90060x+255y=−825$

The coefficient of $x$ in above equation is same and therefore the solutions to the equations can be determined by method of elimination.

The equations can now be solved for y since the coefficient of x is same in both the equations.

$60x+255y−60x−255y=−825−(−900)$

$0=−825+900$

$0=75$

The above obtained results say that $75$ is equal to zero which is incorrect. Hence, the given system of equation is inconsistent.

Chapter 11, Problem 17RE

Chapter 11, Problem 19RE

Chapter 11 Solutions

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