Chapter 13: Q. 9 (page 870)

Solve the system: $\{\begin{matrix} x - 2 y + z = 15 \\ 3 x + y - 3 z = - 8 \\ - 2 x + 4 y - z = - 27 \end{matrix}$

Short Answer

Expert verified

The solution of the given system:

$x = 2 y = - 5 z = 3$

Step by step solution

Step 1. Given information.

System of equations:

\{\begin{matrix} x - 2 y + z = 15 . . . . . . . . . e q u a t i o n (1) \\ 3 x + y - 3 z = - 8 . . . . . . . . . . . e q u a t i o n (2) \\ - 2 x + 4 y - z = - 27 . . . . . . . . . . . e q u a t i o n (3) \end{matrix}

Step 2. Add equation (1) and (3)

$x - 2 y + z - 2 x + 4 y - z = 15 - 27 - x + 2 y = - 12$

$x - 2 y = 12$ ..........equation(4)

Step 3. Substitute the value of equation (4) in to the equation (1).

$12 + z = 15 z = 15 - 12 z = 3$

Step 4. Substitute value of z into the equation (2).

$3 x + y - 3 \times 3 = - 8 3 x + y - 9 = - 8 3 x + y = 9 - 8 3 x + y = 1$

$y = 1 - 3 x$ ...........equation (5)

Step 5. Substitute the value of y from equation (5) into the equation (4).

$x - 2 (1 - 3 x) = 12 x - 2 + 6 x = 12 7 x - 2 = 12 7 x = 12 + 2 7 x = 14 x = \frac{14}{7} x = 2$

Step 6. Substitute the value of x into the equation (5).

$y = 1 - 3 \times 2 y = 1 - 6 y = - 5$

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Solve the system: $\{\begin{matrix} x - 2 y + z = 15 \\ 3 x + y - 3 z = - 8 \\ - 2 x + 4 y - z = - 27 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Add equation (1) and (3)

Step 3. Substitute the value of equation (4) in to the equation (1).

Step 4. Substitute value of z into the equation (2).

Step 5. Substitute the value of y from equation (5) into the equation (4).

Step 6. Substitute the value of x into the equation (5).

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Solve the system:x-2y+z=153x+y-3z=-8-2x+4y-z=-27

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Add equation (1) and (3)

Step 3. Substitute the value of equation (4) in to the equation (1).

Step 4. Substitute value of z into the equation (2).

Step 5. Substitute the value of y from equation (5) into the equation (4).

Step 6. Substitute the value of x into the equation (5).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Solve the system: $\{\begin{matrix} x - 2 y + z = 15 \\ 3 x + y - 3 z = - 8 \\ - 2 x + 4 y - z = - 27 \end{matrix}$