Q16. Solve each system of equations聽... [FREE SOLUTION]

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Chapter 3: Q16. (page 142)

Solve each system of equations
$\begin{array}{l} 4 a + 2 b 鈭� 6 c = 2 \\ 6 a + 3 b 鈭� 9 c = 3 \\ 8 a + 4 b 鈭� 12 c = 6 \end{array}$

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 $4 a + 2 b - 6 c = 2$ by $3$ and multiply the equation $6 a + 3 b - 9 c = 3$ by $2$ .

Perform the subtraction operation on the new two resultant equations.

$\begin{array}{l} \underline{\begin{array}{l} 4 a + 2 b 鈭� 6 c = 2 \\ 6 a + 3 b 鈭� 9 c = 3 \end{array}} 鈥夆赌夆赌夆赌� \begin{matrix} 鈫� multiplyby3 鈫� \\ 鈫� multiplyby2 鈫� \end{matrix} 鈥夆赌夆赌夆赌夆€� \underline{\begin{array}{l} 鈥夆赌夆赌夆赌夆€� 12 a + 6 b 鈭� 18 c = 6 \\ (鈭�) 12 a + 6 b 鈭� 18 c = 6 \end{array}} \\ 鈥夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆赌夆赌夆赌夆€夆€� 0 = 0 \end{array}$

– Conclude the solutions of the given system of equations.

Here, $0 = 0$ . This means the second equation $6 a + 3 b - 9 c = 3$ is a multiple of first equation $4 a + 2 b - 6 c = 2$ .

So, they are the same plane.

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

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91影视

Solve each system of equations
$\begin{array}{l} 4 a + 2 b 鈭� 6 c = 2 \\ 6 a + 3 b 鈭� 9 c = 3 \\ 8 a + 4 b 鈭� 12 c = 6 \end{array}$

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鈭�6c=26a+3b鈭�9c=38a+4b鈭�12c=6

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

Geometry

Decision Maths

Logic and Functions

Statistics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each system of equations
$\begin{array}{l} 4 a + 2 b 鈭� 6 c = 2 \\ 6 a + 3 b 鈭� 9 c = 3 \\ 8 a + 4 b 鈭� 12 c = 6 \end{array}$