AnswersAG Q4 Keystone Algebra 1 Block 25-26 DDiamondUsing Graphs to Determine the Number of Solutions

Using Graphs to Determine the Number of Solutions Answers

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1
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Coretta wants to create a system of equations so that the system has only one solution. Which of these can Coretta do? Check all that apply.

A
Create a pair of equivalent equations.
B
Create a pair of lines in which one line lies directly on top of the other.
C
Create a pair of equations with different slopes.
D
Create a pair of lines that will always stay the same distance apart.
E
Create a pair of lines that intersect at only one point.
2
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Consider the graph with four lines below. By inspection, which system would have no solution?

Question illustration
A
line a and line b
B
line a and line c
C
line b and line c
D
line b and line d
3

The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has no solution?

Question illustration
A
y = negative 5 x + 10
Option A
B
y = 5 (x + 2)
Option B
C
y = 5 (x minus 2)
Option C
D
y = negative 5 x minus 10
Option D
4

The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?

Question illustration
A
y + 1 = 3 x
Option A
B
y = negative 3 x + 1
Option B
C
y = 3 x + 1
Option C
D
y minus 3 x = negative 3
Option D
5

The equations in the system below are equivalent. How many solutions does the system have?

Question illustration
A
no solution
B
one unique solution
C
two solutions
D
an infinite number of solutions
6

The graph below represents a system of equations. By observation, what is the solution to this system?

Question illustration
A
(0, –3)
B
(–3, 0)
C
no solution
D
infinitely many solutions
7

The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has no solution?

Question illustration
A
y = 3 x + 6
Option A
B
y = negative 3 (x + 6)
Option B
C
y = negative 3 (x minus 2)
Option C
D
y = 3 (x minus 2)
Option D
8

The graph for the equation is shown below. If another equation is graphed so that the system has one solution, which equation could that be?

Question illustration
A
y = 2 x minus 4
Option A
B
y = 2 (x + 2)
Option B
C
y = 2 (x minus 4)
Option C
D
y = x + 4
Option D
9

The graphed line shown below is . Which equation, when graphed with the given equation, will form a system that has no solution?

Question illustration
A
y = 4 x + 12
Option A
B
y = negative 4 x
Option B
C
y = negative 12
Option C
D
y = negative 4 (x + 3)
Option D
10

Miguel used the graph below to represent a system of equations. Which statement is the best conclusion for Miguel’s system?

Question illustration
A
Since the lines do not intersect, this system has no solution.
B
Since the lines will intersect at one point, this system has one solution.
C
Since the lines will intersect at two points, this system has two solutions.
D
Since the lines will intersect at many points, the system has many solutions.

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