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Chapter 11: Q. 4 (page 713)

If a system of equations has one solution, the system is and the equations are .

Short Answer

Expert verified

If a system of equations has one solution, the system is consistent and the equations are independent.

Step by step solution

01

Step 1. Given information.

The given statement is:

If a system of equations has one solution, the system is ________ and the equations are ________.

02

Step 2. Determine the missing terms for the blanks.

Consistent and independent: A system of equations is consistent and independent if it has only one solution.

Consistent and dependent: A system of equations is consistent and dependent if it has an infinite number of solutions.

By using the above definitions, it is clear that the required words for the blanks are consistent and independent respectively.

03

Step 3. Conclusion.

If a system of equations has one solution, the system is consistent and the equations are independent.

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Most popular questions from this chapter

In Problems 23–34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

$\{\begin{array}{r} x - 2 y \leq 6 \\ 2 x - 4 y \geq 0 \end{array}$

Graph the equation: $y^{2} = x^{2} - 1$

Fencing: A farmer has 300 feet of fence available to enclose a 4500-square-foot region in the shape of adjoining squares, with sides of length x and y. See the figure. Findx and y.

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$2 x + y - 3 z = 0 - 2 x + 2 y + z = - 7 3 x - 4 y - 3 z = 7$

In Problems 35–42, graph each system of inequalities by hand.

$\{\begin{cases} x^{2} + y^{2} \geq 9 \\ x + y \leq 3 \end{cases}$

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