Chapter 3: Q9. (page 142)

Solve each system of equations.
9.
$\begin{array}{l} x + y + z = 12 \\ 6 x - 2 y - z = 16 \\ 3 x + 4 y + 2 z = 28 \end{array}$

Short Answer

Expert verified

The solution is $x = 4, y = 0, z = 8$ .

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Given system of equations are

$\begin{array}{l} x + y + z = 12 \\ 6 x - 2 y - z = 16 \\ 3 x + 4 y + 2 z = 28 \end{array}$

Multiplying first equation by $2$ and adding to the second first equation, we get

$\begin{array}{l} 2 x + 6 x + 2 z - z = 24 + 16 \\ 8 x + z = 40 \end{array}$

Again multiplying the second equation by $2$ and adding to the third equation, we get

$\begin{array}{l} 12 x + 3 x - 2 z + 2 z = 32 + 28 \\ 15 x = 60 \\ x = 4 \end{array}$

Step-2 –Putting the value of \[x\]in the equation with two variables

$\begin{array}{l} 8 x + z = 40 \\ 8 (4) + z = 40 \\ 32 + z = 40 \\ z = 40 - 32 \\ z = 8 \end{array}$

Step-3 –Substituting the value of x and z in the equation with three variables

$\begin{array}{l} x + y + z = 12 \\ 4 + y + 18 = 12 \\ y = 12 - 12 \\ y = 0 \end{array}$

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Solve each system of equations.
9.
$\begin{array}{l} x + y + z = 12 \\ 6 x - 2 y - z = 16 \\ 3 x + 4 y + 2 z = 28 \end{array}$

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Step-2 –Putting the value of \[x\]in the equation with two variables

Step-3 –Substituting the value of x and z in the equation with three variables

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Solve each system of equations.9.x+y+z=126x−2y−z=163x+4y+2z=28

Short Answer

Step by step solution

Step-1 –Using elimination to obtain two equations with two variables

Step-2 –Putting the value of \[x\]in the equation with two variables

Step-3 –Substituting the value of x and z in the equation with three variables

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

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Calculus

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
9.
$\begin{array}{l} x + y + z = 12 \\ 6 x - 2 y - z = 16 \\ 3 x + 4 y + 2 z = 28 \end{array}$