Chapter 3: Q19. (page 143)

Solve each system of equations
$\begin{array}{l} 4 a - 2 b + 8 c = 30 \\ a + 2 b - 7 c = - 12 \\ 2 a - b + 4 c = 15 \end{array}$

Short Answer

Expert verified

The solution set of the given system of equations is infinitely many solutions.

Step by step solution

– Use the elimination method to get the system of equations in two variables.

Multiply the equation $2 a - b + 4 c = 15$ by $2$ and add the new resultant equation to the equation $4 a - 2 b + 8 c = 30$ .

Perform the subtraction operation on the new two resultant equations

$\begin{array}{l} \underline{\begin{array}{l} 2 a - b + 4 c = 15 \\ 4 a - 2 b + 8 c = 30 \end{array}} \begin{matrix} \to multiplyby2 \to \end{matrix} \underline{\begin{array}{l} 4 a - 2 b + 8 c = 30 \\ (-) 4 a - 2 b + 8 c = 30 \end{array}} \\ 0 = 0 \end{array}$

– Conclude the solutions of the given system of equations.

Here, $0 = 0$ . This means the third equation $2 a - b + 4 c = 15$ is a multiple of first equation $4 a - 2 b + 8 c = 30$ .

So, they are the same plane.

Hence, the solution of the given system of equations is infinitely many solutions

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Solve each system of equations
$\begin{array}{l} 4 a - 2 b + 8 c = 30 \\ a + 2 b - 7 c = - 12 \\ 2 a - b + 4 c = 15 \end{array}$

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Conclude the solutions of the given system of equations.

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Solve each system of equations4a−2b+8c=30a+2b−7c=−122a−b+4c=15

Short Answer

Step by step solution

– Use the elimination method to get the system of equations in two variables.

– Conclude the solutions of the given system of equations.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Applied Mathematics

Geometry

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations
$\begin{array}{l} 4 a - 2 b + 8 c = 30 \\ a + 2 b - 7 c = - 12 \\ 2 a - b + 4 c = 15 \end{array}$