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Chapter 11: Q. 3 (page 713)

If a system of equations has no solution, it is said to be _______.

Short Answer

Expert verified

If a system of equations has no solution, it is said to be inconsistent.

Step by step solution

01

Step 1. Given information.

The given statement is:

If a system of equations has no solution, it is said to be _______.

02

Step 2. Determine the missing term for the blank.

Inconsistent: A system of equations is inconsistent if it has no solution.

Consistent: A system of equations is consistent if it has at least one solution.

By using the above definitions, it is clear that the required word for the blank is inconsistent.

03

Step 3. Conclusion.

If a system of equations has no solution, it is said to be inconsistent.

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Most popular questions from this chapter

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

$\{\begin{matrix} 3 x - y = 7 \\ 9 x - 3 y = 21 \end{matrix}$

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

x + 2y - z = -3

2x - 4y + z = -7

-2x + 2y - 3z = 4

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

$\{\begin{matrix} x - y = 5 \\ - 3 x + 3 y = 2 \end{matrix}$

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.

$y = 3 x - 5; x^{2} + y^{2} = 5$

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