Chapter 4: Q 4.70 (page 429)

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

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,

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

Step 2. Solving the equations

Adding first and second equation, we get

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

Now, multiplying by $3$ in second equation, we get

role="math" localid="1644580632346" $3 (- x + 2 y - 3 z) = 3 (- 4) - 3 x + 6 y - 9 z = - 12 - (5)$

Now, subtracting third and fifth equation, we get

$- 3 x + 3 x + 6 y - 2 y - 9 z - 7 z = - 12 + 0 4 y - 16 z = - 12 y - 4 z = - 3 - (6)$

Now, subtracting sixth and fourth equation, we get

$y - y - 4 z + 4 z = - 3 + 3 0 = 0$

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the equations

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Solve the system by equations:x−y−z=1−x+2y−3z=−43x−2y−7z=0

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

Probability and Statistics

Mechanics Maths

Calculus

Geometry

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

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