Number of Solutions by Graphs

1.3 Part 2: Determinining the Number of Solutions to a System of Equations

​EQ: How can you solve a systems of equations by graphing?

Multiple Choice

The solution to the system is

• (-2, -8)
• (-8, -2)
• (2, -8)

Multiple Choice

The solution is ...

• (3, -6)
• (-3, -6)
• (-6, 3)
• No solution

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

Graph to find the solution to the system of equations: 

6x + 7y = 20

y = 2x 

• (-1 , -2)

• (1 , 2) 

• (2 , 1) 

• (1 , 1)

Multiple Choice

Graph to find the solution to the system of equations: 

-4x + 2y = 14

y = 6x + 11

• (-1 , -5)

• (1 , 5) 

• (4 , 1) 

• (-1 , 5)

Multiple Choice

Graph to find the solution to the system of equations: 

y = 4

x = -6

• (-6 , -4)

• (-6 , 4) 

• (4 , -6) 

• (-4 , 6)

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• the same line

Multiple Choice

If a system of equations has one solution, what does the graph look like? 

• intersecting lines
• parallel lines
• the same line

Multiple Choice

If a system of equations has infinity many solutions, what does the graph look like? 

• intersecting lines
• parallel lines
• the same line

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

What is the number of solutions to the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• Infinitely Many Solutions

Multiple Choice

Graph to determine the number of solutions:

y = -x + 4

y = -x + 2

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Graph to determine the number of solutions:

y = 4x + 3

y = x - 6

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Graph to determine the number of solutions:

y = x

y = -x

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Graph to determine the number of solutions:

x + y = 10

y = -x + 10

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

When trying to determine the number of solutions without graphing, both lines should be in what form?

• Slope Intercept Form

• Standard Form

• Either

Multiple Choice

T/F? Parallel Lines have the same slopes and different y-intercepts

• True

• False

Multiple Choice

T/F? Intersecting Lines have different slopes and y-intercepts

• True

• False

Multiple Choice

Why will this system have infinite solutions?

• The equations are both negative.

• The equations are the SAME, they have the same slope and y-intercept.

• They have the same y-intercept but not the same slope.

• They have the same slope but not the same y-intercept.

Multiple Choice

Without graphing, determine the number of solutions.

4x + 2y = 10

y = -2x

• One Solution 

• No Solution

• Infinitely Many Solutions

Multiple Choice

Without graphing, determine the number of solutions.

x + y = 8

x - y = 4

• One Solution 

• No Solution

• Infinitely Many Solutions

Multiple Choice

Without graphing, determine the number of solutions.

3y = 6x - 3

y = 2x - 1

• One Solution 

• No Solution

• Infinitely Many Solutions