Chapter 4: Q 4.68 (page 428)

Solve the system of equations:
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

Short Answer

Expert verified

There is no solution of given system of linear equations.

Step by step solution

Step 1. Given Information

We are given a system of linear equation,

$2 x - 2 y + 3 z = 6 - (1) 4 x - 3 y + 2 z = 0 - (2) - 2 x + 3 y - 7 z = 1 - (3)$

Step 2. Solving the equations

Adding first and third equation, we get

$2 x - 2 x - 2 y + 3 y + 3 z - 7 z = 6 + 1 y - 4 z = 7 - (4)$

Multiplying by $2$ in first equation and subtraction it from second equation,

$2 (2 x - 2 y + 3 z) = 2 (6) 4 x - 4 y + 12 z = 12$

Subtracting, we get

role="math" localid="1644577982732" $4 x - 4 x - 4 y + 3 y + 6 z - 2 z = 12 - 0 - y + 4 z = 12 - (5)$

Now, adding fourth and fifth equation, we get

$y - y - 4 z + 4 z = 7 + 12 0 \neq 19$

This is not true hence the given system has no solution.

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Solve the system of equations:
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the equations

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Solve the system of equations:2x−2y+3z=64x−3y+2z=0−2x+3y−7z=1

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

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Study anywhere. Anytime. Across all devices.

Solve the system of equations:
$2 x - 2 y + 3 z = 6 4 x - 3 y + 2 z = 0 - 2 x + 3 y - 7 z = 1$