Chapter 3: Q8. (page 142)

Solve each system of equations.
$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$

Short Answer

Expert verified

The solution is not possible.

Step by step solution

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

Given system of equations are

$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$

Multiplying first equation by $4$ and adding to the second equation, we get

localid="1648720251666" $\begin{array}{l} 8 x + x - 4 y + 2 y = 4 + 3 \\ 9 x - 2 y = 7 \end{array}$

Again multiplying first equation by $7$ and adding to the third equation, we get

$\begin{array}{l} 14 x + 4 x - 7 y + 3 y = 7 - 8 \\ 18 x - 4 y = - 1 \end{array}$

Step-2 –Solving the system of two equations with two variables

System of two equations with two variables are

$\begin{array}{l} 9 x - 2 y = 7 \\ 18 x - 4 y = - 1 \end{array}$

Step-3- Solve the second equation

$\begin{array}{l} 18 x - 4 y = - 1 \\ 2 (9 x - 4 y) = - 1 \\ 2 (7) = - 1 \\ 14 = - 1 \end{array}$

Which is not possible.

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Solve each system of equations.
$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$

Short Answer

Step by step solution

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

Step-2 –Solving the system of two equations with two variables

Step-3- Solve the second equation

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Solve each system of equations.2x−y+z=1x+2y−4z=34x+3y−7z=−8

Short Answer

Step by step solution

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

Step-2 –Solving the system of two equations with two variables

Step-3- Solve the second equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Mechanics Maths

Probability and Statistics

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Calculus

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{array}{l} 2 x - y + z = 1 \\ x + 2 y - 4 z = 3 \\ 4 x + 3 y - 7 z = - 8 \end{array}$