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Q73.

Expert-verified

Algebra 2

Found in: Page 228

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Solve the following system of equations?
$\begin{matrix} a + b + c = 6 \\ 2 a - b + 3 c = 16 \\ a + 3 b - 2 c = - 6 \end{matrix}$

The solution for the system of equations is $a = 2, b = 0, c = 4$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given system of equations are,

$\begin{matrix} a + b + c = 6.... (1) \\ 2 a - b + 3 c = 16.... (2) \\ a + 3 b - 2 c = - 6.... (3) \end{matrix}$

Step 2. Calculation.

Multiply (1) by 2 and subtract from (2) gives,

$\begin{matrix} (2 a - b + 3 c) - (2 a + 2 b + 2 c) = 16 - 12 \\ (2 a - b + 3 c) - (2 a + 2 b + 2 c) = 4 \\ - 3 b + c = 4.... (4) \end{matrix}$

Subtract (3) from (1) gives,

$\begin{matrix} (a + b + c) - (a + 3 b - 2 c) = 6 + 6 \\ - 2 b + 3 c = 12 .... (5) \end{matrix}$

Multiply (4) by 3 and subtract from (5) gives,

$\begin{matrix} (- 2 b + 3 c) - (- 9 b + 3 c) = 12 - 12 \\ 7 b = 0 \\ b = 0 \end{matrix}$

Plugging $b = 0$ in (4) gives $c = 4$ .

Again plugging $b = 0$ and $c = 4$ in (1),

$\begin{matrix} a + b + c = 6.... (From (1)) \\ a + (0) + (4) = 6.... (\begin{array}{l} Plugging \\ b = 0, c = 4 \end{array}) \\ a = 2 \end{matrix}$

Step 3. Conclusion.

The solution for the system of equations is $a = 2, b = 0, c = 4$ .

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