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Chapter 6: Q11. (page 389)

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

x鈭�y=1x+y=5

Short Answer

Expert verified

The graph of the system is

The number of solutions is 1 and name of the solution is 3,2.

Step by step solution

01

Step 1. Graph the system of equations.

The given system of equation is:

x鈭�y=1 鈥� (1)

x+y=5 鈥� (2)

The graph of two equations is drawn as below.

02

Step 2. Determine the number of solutions.

From the graph it can be observed that the two lines intersect at exactly one point. This intersection point of two lines is nothing but the solution set of given system of equation. Therefore, number of solutions of the set of equations if 1.

03

Step 3. Name the solutions, if possible.

Now the intersection point of two straight lines shown by eq. (1) and (2) is 3,2. Therefore, one solution of given system of equation is labelled as 3,2.

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Most popular questions from this chapter

Use elimination to solve each system of equations.

鈭�9x+3y=鈭�33x鈭�2y=鈭�4

The cost of two groups going to an amusement park is shown in the table.

Group
Total Cost
4adults,2children
\(184
localid="1647549424859" 4adults,localid="1647549450994" 3children
\)200

a. Define variables to represent the cost of an adult ticket and the cost of a child ticket.

b. Write a system of equations to find the cost of an adult ticket and the cost of a child ticket.

c. Solve the systems of equations, and explain what the solution means.

d. How much will a group of 3 adults and 5 children be charged for admission?

Write an inequality for the graph below.

Use elimination method to solve the system of equations below:

3x+2y=鈭�22x鈭�2y=鈭�18

A (1,3) B (7,鈭�4) C (鈭�2,鈭�3) D (鈭�4,5)

Use an augmented matrix to solve each system of equations.

2x鈭�4y=10x+2y=5
See all solutions

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