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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鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

x+4y鈮�8x+4y鈮�4

Running a Race : In a 1-mile race, the winner crosses the finish line 10 feet ahead of the second-place runner and 20 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner?

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

x-y-z=12x+3y+z=23x+2y=0

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

x+2y=42x+4y=8

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

xy=4;x2+y2=8
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