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Chapter 6: Q16. (page 389)

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

3x+y=56x=10鈭�2y

Short Answer

Expert verified

The graph of the system is

The number of solutions is infinitely many.

Step by step solution

01

Step 1. Graph the system of equations.

The given system of equation is:

3x+y=5 鈥� (1)

6x=10鈭�2y 鈥� (2)

The graph of two equations is drawn as below.

02

Step 2. Interpret the system of equations and graph.

Rewrite the given system of equation:

3x+y=5y=鈭�3x+5鈥�1

6x=10鈭�2y2y=鈭�6x+10y=鈭�3x+5鈥�2

The two equations represented eq. (1) and (2) are same. That鈥檚 why there is a single line in graph of two equations as they are overlapping with each other.

03

Step 3. Name the solutions, if possible.

When a graph of two equations gives a same line of graph, it contains the infinite number of solutions.

Therefore, infinite number of solutions is observed for given system of equation and hence naming all the solutions is not possible.

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Most popular questions from this chapter

Use elimination to solve each system of equations.

8x鈭�3y=鈭�353x+4y=33

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

x鈭�4y=鈭�6y=鈭�1

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

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

Use an augmented matrix to solve each system of equations.

x鈭�y=53x+3y=3

State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.

A constant by which you multiply a matrix is called a scalar.
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