Chapter 3: Q17. (page 149)

Solve each system of equations.
$\begin{matrix} x + y + z = - 1 \\ 2 x + 4 y + z = 1 \\ x + 2 y - 3 z = - 3 \end{matrix}$

Short Answer

Expert verified

The solution of the given equation is $x = - 4, y = 2$ and $z = 1.$

Step by step solution

– Use elimination method to make a system of two equations in two variables

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

$\begin{array}{r} .... (1) \\ .... (2) \\ .... (3) \end{array}$

Multiplying equation (1) by 2, we get

$2 x + 2 y + 2 z = - 2$

$.... (4)$

Subtracting (1) from (4), we get

$\begin{matrix} (2 x + 2 y + 2 z + 2) - (2 x + 4 y + z - 1) = 0 \\ 2 x + 2 y + 2 z + 2 - 2 x - 4 y - z + 1 = 0 \\ - 2 y + z + 3 = 0 \\ 2 y - z - 3 = 0 \\ 2 y - z = 3 \end{matrix}$

$.... (5)$

Subtracting (3) from (1), we get

$\begin{matrix} (x + y + z + 1) - (x + 2 y - 3 z + 3) = 0 \\ x + y + z + 1 - x - 2 y + 3 z - 3 = 0 \\ - y + 4 z - 2 = 0 \\ y - 4 z + 2 = 0 \\ y - 4 z = - 2 \end{matrix}$

$.... (6)$

– Solve the system of two equations

Multiplying (6) by 2, we get

$2 y - 8 z = - 4$

$.... (7)$

Subtracting (7) from (5), we get

$\begin{matrix} (2 y - z - 3) - (2 y - 8 z + 4) = 0 \\ 2 y - z - 3 - 2 y + 8 z - 4 = 0 \\ 7 z - 7 = 0 \\ 7 z = 7 \\ z = 1 \end{matrix}$

Substituting the value of in (5), we get

$\begin{matrix} 2 y - z = 3 \\ 2 y - 1 = 3 \\ 2 y = 3 + 1 \\ 2 y = 4 \\ y = 2 \end{matrix}$

– Evaluate the value of x

Substituting the value of $z$ and $y$ in (1), we get

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

Thus, the values are $x = - 4, y = 2$ and $z = 1.$

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Solve each system of equations.
$\begin{matrix} x + y + z = - 1 \\ 2 x + 4 y + z = 1 \\ x + 2 y - 3 z = - 3 \end{matrix}$

Short Answer

Step by step solution

– Use elimination method to make a system of two equations in two variables

– Solve the system of two equations

– Evaluate the value of x

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Solve each system of equations.x+y+z=−12x+4y+z=1x+2y−3z=−3

Short Answer

Step by step solution

– Use elimination method to make a system of two equations in two variables

– Solve the system of two equations

– Evaluate the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{matrix} x + y + z = - 1 \\ 2 x + 4 y + z = 1 \\ x + 2 y - 3 z = - 3 \end{matrix}$