Determine Number of Solutions to a System of Equations

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

y= -3x + 2

3x + y = 2

• Infinite Number of Solutions

• No Solution

• One Solution

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

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

• Parallel lines

• the same line

• Intersecting lines

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

• Intersecting lines

• Identical lines

• Parallel lines

If a system of linear equations has infinitely many solutions, the equations will have

• the same slope and different y-int

• the same slope and same y-int

• different slopes

• same y-int

If a system of linear equations has one solution, the equations will have

• same slopes

• same y-ints

• different slopes

• different y -int

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

What is the solution to this system?

• One Solution

• No solution

• Infinitely Many Solutions

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