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Chapter 3: Q9. (page 142)

Solve each system of equations.

9.

x+y+z=126x鈭�2y鈭�z=163x+4y+2z=28

Short Answer

Expert verified

The solution is x=4,y=0,z=8.

Step by step solution

01

Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

x+y+z=126x鈭�2y鈭�z=163x+4y+2z=28

Multiplying first equation by 2and adding to the second first equation, we get

2x+6x+2z鈭�z=24+168x+z=40

Again multiplying the second equation by 2and adding to the third equation, we get

12x+3x鈭�2z+2z=32+2815x=60x=4

02

Step-2 –Putting the value of \[x\]in the equation with two variables

8x+z=408(4)+z=4032+z=40z=40鈭�32z=8

03

Step-3 –Substituting the value of x and z in the equation with three variables

x+y+z=124+y+18=12y=12鈭�12y=0

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Most popular questions from this chapter

Give an example of a system of equations that is consistent and independent.

11: Solve each system of inequalities by graphing.

x+2y鈮�73x-4y>12

Choose the letter of the term that best matches each phase.

10. A region in which no maximum value exists

Explain why a system of linear equations cannot have exactly two solutions.

12(x+4)=34
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