Q17. Solve each system of equations.x... [FREE SOLUTION]

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Chapter 3: Q17. (page 149)

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

Short Answer

Expert verified

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

Step by step solution

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

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

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

Multiplying equation (1) by 2, we get

$2 x + 2 y + 2 z = 鈭� 2$

$.... (4)$

Subtracting (1) from (4), we get

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

$.... (5)$

Subtracting (3) from (1), we get

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

$.... (6)$

– Solve the system of two equations

Multiplying (6) by 2, we get

$2 y 鈭� 8 z = 鈭� 4$

$.... (7)$

Subtracting (7) from (5), we get

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

Substituting the value of in (5), we get

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

– Evaluate the value of x

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

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

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

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

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

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

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

Probability and Statistics

Discrete Mathematics

Statistics

Decision Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

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