b. Use the graphs you have drawn to complete each statement: y=x-6 y=-x+5 a. The solution set of the system of equations is b. Write a system of equations for which the solution set is the empty set (0) c. Write a system of equations for which the solution set has infinitely many ordered pairs, and use set builder notation to describe the solution set.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
a. Carefully draw the graphs of the four lines given by the equations below. Label at least two points on each line, using
ordered pairs. Label each line with its name (L₁, L2, L3 or L4).
L₁: y=x-6
-12 -11 -10 -9
L2:2x-6y=-6
-8 -7 -6 -5 -4 -3
-2
-1
a. The solution set of the system of equations
8
7
6
5
4
3
2
1
-1
-2
-3
-6
-7
y
1
2
b. Use the graphs you have drawn to complete each statement:
y = x-6
y=- -x+5
10
L3: y=-x+5
3
is
4
5
b. Write a system of equations for which the solution set is the empty set (0)
6
7
8
9
L4:3x 9y = 54
10
-
11
X
12
c. Write a system of equations for which the solution set has infinitely many ordered pairs, and use set builder notation
to describe the solution set.
Transcribed Image Text:a. Carefully draw the graphs of the four lines given by the equations below. Label at least two points on each line, using ordered pairs. Label each line with its name (L₁, L2, L3 or L4). L₁: y=x-6 -12 -11 -10 -9 L2:2x-6y=-6 -8 -7 -6 -5 -4 -3 -2 -1 a. The solution set of the system of equations 8 7 6 5 4 3 2 1 -1 -2 -3 -6 -7 y 1 2 b. Use the graphs you have drawn to complete each statement: y = x-6 y=- -x+5 10 L3: y=-x+5 3 is 4 5 b. Write a system of equations for which the solution set is the empty set (0) 6 7 8 9 L4:3x 9y = 54 10 - 11 X 12 c. Write a system of equations for which the solution set has infinitely many ordered pairs, and use set builder notation to describe the solution set.
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