Chapter 3: Q26. (page 148)

26: Solve each system of equations.
$\begin{matrix} x + 4 y - z = 6 \\ 3 x + 2 y + 3 z = 16 \\ 2 x - y + z = 3 \end{matrix}$

Short Answer

Expert verified

The solution is $x = 1, y = 2, z = 3$ .

Step by step solution

Step-1 – Use elimination to make a system of two equations in two variables.

Given equations are-:

$\begin{matrix} x + 4 y - z = 6...... (1) \\ 3 x + 2 y + 3 z = 16....... (2) \\ 2 x - y + z = 3....... (3) \end{matrix}$

Multiplying the first equation by $3$ and subtracting with second equation, we get

$\begin{matrix} 12 y - 2 y - 3 z - 3 z = 18 - 16 \\ 10 y - 6 z = 2........ (4) \end{matrix}$

Again, multiplying the first equation by $2$ and subtracting with third equation, we get

$\begin{matrix} 8 y + y - 2 z - z = 12 - 3 \\ 9 y - 3 z = 9........ (5) \end{matrix}$

Step-2 – Solve the system of two equations.

$\begin{matrix} 10 y - 6 z = 2....... (4) \\ 9 y - 3 z = 9........ (5) \end{matrix}$

Multiplying the fifth equation by $2$ and subtracting from fourth equation.

$\begin{matrix} 10 y - 18 y = 2 - 18 \\ - 8 y = - 16 \\ y = 2 \end{matrix}$

Putting the value of $y$ in the fourth equation, we get

$\begin{matrix} 10 y - 6 z = 2 \\ 10 (2) - 6 z = 2 \\ - 6 z = 2 - 20 \\ - 6 z = - 18 \\ z = 3 \end{matrix}$

Step-3 – Substituting the value according to the coordinates in one of the equations with three variables.

$\begin{matrix} x + 4 y - z = 6 \\ x + 4 (2) - 3 = 6 \\ x + 8 - 3 = 6 \\ x = 1 \end{matrix}$

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26: Solve each system of equations.
$\begin{matrix} x + 4 y - z = 6 \\ 3 x + 2 y + 3 z = 16 \\ 2 x - y + z = 3 \end{matrix}$

Short Answer

Step by step solution

Step-1 – Use elimination to make a system of two equations in two variables.

Step-2 – Solve the system of two equations.

Step-3 – Substituting the value according to the coordinates in one of the equations with three variables.

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26: Solve each system of equations.x+4y-z=63x+2y+3z=162x-y+z=3

Short Answer

Step by step solution

Step-1 – Use elimination to make a system of two equations in two variables.

Step-2 – Solve the system of two equations.

Step-3 – Substituting the value according to the coordinates in one of the equations with three variables.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Probability and Statistics

Calculus

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

26: Solve each system of equations.
$\begin{matrix} x + 4 y - z = 6 \\ 3 x + 2 y + 3 z = 16 \\ 2 x - y + z = 3 \end{matrix}$