Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 4: Q 4.69 (page 429)

Solve the system by equations:
$x + y 鈭� z = 0 2 x + 4 y 鈭� 2 z = 6 3 x + 6 y 鈭� 3 z = 9$

Short Answer

Expert verified

There are infinitely many number of solutions of given system of equations.

Step by step solution

Step 1. Given Information

We are given a system of linear equation,

$x + y 鈭� z = 0 - (1) 2 x + 4 y 鈭� 2 z = 6 - (2) 3 x + 6 y 鈭� 3 z = 9 - (3)$

Step 2. Solving the equations

Multiplying by $3$ in second equation and $2$ in third equation, we get

localid="1644580091504" $3 (2 x + 4 y - 2 z) = 3 (6) 6 x + 12 y - 6 z = 18 - (4)$

$2 (3 x + 6 y - 3 z = 2 (9) 6 x + 12 y - 6 z = 18 - (5)$

Now, subtracting the fourth and fifth equations, we get

$6 x - 6 x + 12 y - 12 y - 6 z + 6 z = 18 - 18 0 = 0$

This is true, hence the system has infinitely many solutions.

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91影视

Solve the system by equations:
$x + y 鈭� z = 0 2 x + 4 y 鈭� 2 z = 6 3 x + 6 y 鈭� 3 z = 9$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the equations

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91影视

Solve the system by equations:x+y鈭�z=02x+4y鈭�2z=63x+6y鈭�3z=9

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Probability and Statistics

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Solve the system by equations:
$x + y 鈭� z = 0 2 x + 4 y 鈭� 2 z = 6 3 x + 6 y 鈭� 3 z = 9$