Solving Systems of Equations by Graphing

Which equation represents the following graph?

• y = 3x + 2
• y = -2x + 3
• y = 2x + 3
• y = -3x + 2

What is the solution to this system?

• (1, -1)
• (-1, 1)
• (0, -2)
• (2, 0)

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

If a system of linear equations has one solution, what does this mean about the two lines? 

• Parallel lines
• the same line 
• Intersecting lines

What is the solution to this system?

• One Solution
• No solution
• Infinitely Many Solutions

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Based on the equations for each line, determine how many solutions the system would have.

y=2x+3

y=-4x+3

• Infinite Number of Solutions

• No Solution

• One Solution

Based on the equations for each line, determine how many solutions the system would have.

y=5x+3

y=5x-2

• Infinite Number of Solutions

• No Solution

• One Solution

Based on the equations for each line, determine how many solutions the system would have.

y=-3x+2

y=-3x+2

• Infinite Number of Solutions

• No Solution

• One Solution

Solve the following system by graphing.  What is the solution?

• Infinite number of solutions
• (3, 3)
• (3, -3)
• (-3, 3)