Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.5, Problem 14PPS
To determine

To calculate: The solution set of system of equations,

  8x+3y+6z=43−3x+5y+2z=325x−2y+5z=24

Expert Solution & Answer
Check Mark

Answer to Problem 14PPS

The solution set of the system of equations is (−1,3,7) .

Explanation of Solution

Given information:

The system of equations is provided below,

  8x+3y+6z=43−3x+5y+2z=325x−2y+5z=24

Formula used:

A system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.

Calculation:

Consider the provided system of equations as,

  8x+3y+6z=43−3x+5y+2z=325x−2y+5z=24

Recall that a system of equations with three variables can be solved by elimination method and substitution method. Select any two pairs of equations from the system and eliminate the same variable by adding or subtracting and then simplify it.

So, multiply the third equation by 3 and second equation by 5 and then add both the resulting equations to eliminate x .

  3(5x−2y+5z)=3(24)15x−6y+15z=72

  5(−3x+5y+2z)=5(32)−15x+25y+10z=160

Now add both the resulting equations as,

  15x−6y+15z=72(+)−15x+25y+10z=16019y+25z=232

Now, multiply first equation by 3 and multiply second equation by 8 and add resulting equations to eliminate x ,

  3(8x+3y+6z)=3(43)24x+9y+18z=129

  8(−3x+5y+2z)=8(32)−24x+40y+16z=256

Add both the resulting equations as,

  24x+9y+18z=129(+)−24x+40y+16z=25649y+34z=385

Multiply 19y+25z=232 by −49 and 49y+34z=385 by 19 and add resulting equations to eliminate yas ,

  −49(19y+25z)=−49(232)−931y−1225z=−11368

  19(49y+34z)=19(385)931y+646z=7315

Add both the equations and solve to find the value of z ,

  −931y−1225z=−11368(+)931y+646z=7315−579z=−4053

Simplify −579z=−4053 as,

  −579z=−4053z=−4053−579z=7

Substitute z=7 in 19y+25z=232 to get the value of y ,

  19y+25(7)=23219y+175=23219y=57y=3

Now, substitute y=3 and z=7 in equation second to get the value of x as,

  −3x+5(3)+2(7)=32−3x+15+14=32−3x=3x=−1

To check whether the solution set is correct, substitute the values of x , y and zin first equation as,

  8x+3y+6z=438(−1)+3(3)+6(7)=43−8+9+42=4343=43

Since, left-hand side is equal to right-hand side; the solution set is true for all the equations.

Thus, the solution set of the system of equations is (−1,3,7) .

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Chapter 3.5, Problem 13PPS
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Chapter 3.5, Problem 15PPS

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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