Chapter 4: Q52. (page 166)

Solve each system of equations.
$\begin{matrix} 6 x - 2 y - 3 z = - 10 \\ - 6 x + y + 9 z = 3 \\ 8 x - 3 y = - 16 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations: $\begin{matrix} 6 x - 2 y - 3 z = - 10 \\ - 6 x + y + 9 z = 3 \\ 8 x - 3 y = - 16 \end{matrix}$ is $(\frac{1}{4}, 6, - \frac{1}{6})$ .

Step by step solution

- Use elimination method

Let the equations be:

$6 x - 2 y - 3 z = - 10$ … (i)

$- 6 x + y + 9 z = 3$ … (ii)

$8 x - 3 y = - 16$ … (iii)

Use elimination to make a system of two equations (i) and (ii) in two variables. Multiply first equation by 3 and then add it with equation (ii) to eliminate variable z.

$\begin{array}{l} 18 x - 6 y - 9 z = - 30 \\ \underline{- 6 x + y + 9 z = 3} \\ 12 x - 5 y = - 27 \end{array}$

- Solve the system of equations in two variables

Solve the system of equations $8 x - 3 y = - 16$ and $12 x - 5 y = - 27$ . Multiply first equation by 3 and second equation by 2 then subtract the two equations.

$\begin{array}{l} 24 x - 9 y = - 48 \\ \underline{- 24 x - 10 y = - 54} \\ y = 6 \end{array}$

- Solve for variable x

Now substitute 6 for y into the equation $8 x - 3 y = - 16$ .

$\begin{matrix} 8 x - 3 (6) = - 16 \\ 8 x - 18 + 18 = - 16 + 18 \\ 8 x = 2 \\ x = \frac{1}{4} \end{matrix}$

- Solve for variable z

Now substitute $\frac{1}{4}$ for x and 6 for y into the equation $6 x - 2 y - 3 z = - 10$ .

$\begin{matrix} 6 (\frac{1}{4}) - 2 (6) - 3 z = - 10 \\ \frac{3}{2} - 12 - 3 z = - 10 \\ - \frac{21}{2} - 3 z + \frac{21}{2} = - 10 + \frac{21}{2} \\ - 3 z = \frac{- 20 + 21}{2} \\ - 3 z = \frac{1}{2} \\ z = - \frac{1}{6} \end{matrix}$

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Solve each system of equations.
$\begin{matrix} 6 x - 2 y - 3 z = - 10 \\ - 6 x + y + 9 z = 3 \\ 8 x - 3 y = - 16 \end{matrix}$

Short Answer

Step by step solution

- Use elimination method

- Solve the system of equations in two variables

- Solve for variable x

- Solve for variable z

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Solve each system of equations.6x−2y−3z=−10−6x+y+9z=38x−3y=−16

Short Answer

Step by step solution

- Use elimination method

- Solve the system of equations in two variables

- Solve for variable x

- Solve for variable z

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{matrix} 6 x - 2 y - 3 z = - 10 \\ - 6 x + y + 9 z = 3 \\ 8 x - 3 y = - 16 \end{matrix}$