Chapter 5: Q73. (page 228)

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

Short Answer

Expert verified

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

Step by step solution

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

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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Solve the following system of equations?a+b+c=62a−b+3c=16a+3b−2c=−6

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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