Chapter 3: Q18. (page 149)

Solve each system of equations.
$\begin{matrix} x + z = 7 \\ 2 y - z = - 3 \\ - x - 3 y + 2 z = 11 \end{matrix}$

Short Answer

Expert verified

The solution of the given equation $x = - 2, y = 3$ is and $z = 9.$

Step by step solution

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

$\begin{matrix} x + z = 7 \\ 2 y - z = - 3 \\ - x - 3 y + 2 z = 11 \end{matrix}$

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

Adding (1) and (3), we get

$\begin{matrix} (x + z - 7) + (- x - 3 y + 2 z - 11) = 0 \\ x + z - 7 - x - 3 y + 2 z - 11 = 0 \\ 3 z - 3 y - 18 = 0 \\ 3 z - 3 y = 18 \\ 3 (z - y) = 18 \\ z - y = 6 \end{matrix}$

$.... (4)$

– Solve the system of two equations

Adding (2) and (4), we get

$\begin{matrix} (2 y - z + 3) + (z - y - 6) = 0 \\ 2 y - z + 3 + z - y - 6 = 0 \\ y - 3 = 0 \\ y = 3 \end{matrix}$

$.... (5)$

Substituting in equation (4), we get

$\begin{matrix} z - y = 6 \\ z - 3 = 6 \\ z = 9 \end{matrix}$

– Evaluate the value of x

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

$\begin{matrix} x + z = 7 \\ x + 9 = 7 \\ x = - 2 \end{matrix}$

Thus, the values are $x = - 2, y = 3$ and $z = 9.$

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Solve each system of equations.
$\begin{matrix} x + z = 7 \\ 2 y - z = - 3 \\ - x - 3 y + 2 z = 11 \end{matrix}$

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+z=72y−z=−3−x−3y+2z=11

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

Logic and Functions

Statistics

Pure Maths

Discrete Mathematics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations.
$\begin{matrix} x + z = 7 \\ 2 y - z = - 3 \\ - x - 3 y + 2 z = 11 \end{matrix}$