Chapter 11: Q. 30 (page 714)

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} 3 x - y = 7 \\ 9 x - 3 y = 21 \end{matrix}$

Short Answer

Expert verified

The given system of equations has infinite number of solutions.

Step by step solution

Step 1. Given information.

The given equations are:

$\begin{array}{rcl} 3 x - y & = & 7 \\ 9 x - 3 y & = & 21 \end{array}$

Step 2. Determine one variable in terms of another variable.

The first equation can be written as:

$\begin{array}{rcl} 3 x - y & = & 7 \\ - y & = & 7 - 3 x \\ y & = & - (7 - 3 x) \\ y & = & 3 x - 7 \end{array}$

Step 3. Determine the value of one variable.

Substitute the above value in the second equation.

$\begin{array}{rcl} 9 x - 3 (3 x - 7) & = & 21 \\ 9 x - 9 x + 21 & = & 21 \\ 21 & = & 21 \end{array}$

This statement is true for all real values. So, the given system of equations has infinite number of solutions.

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Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} 3 x - y = 7 \\ 9 x - 3 y = 21 \end{matrix}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine one variable in terms of another variable.

Step 3. Determine the value of one variable.

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Solve each system of equations. If the system has no solution, say that it is inconsistent.3x-y=79x-3y=21

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine one variable in terms of another variable.

Step 3. Determine the value of one variable.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Statistics

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$\{\begin{matrix} 3 x - y = 7 \\ 9 x - 3 y = 21 \end{matrix}$