Solving pairs of linear equations in two variables

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

y=x+2

y=x-5

• Infinite Number of Solutions

• No Solution

• One Solution

• Infinite solutions

• No solution

• Exactly one solution

• Exactly two solutions

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

The system of equations

y = 3x + 2

y = 3x + 6

has how many solutions?

• no solution

• infinitely many solutions

• one solution

•  One Solution 

• No Solution

• Infinite Solutions

How many solutions does a system of parallel lines have?

• None

• One

• Two

• Infinitely Many

How many solutions will the following system of equations have?

 $-12x-3y=-1$  and  $y=-4x+2$  

• one solution

• no solution

• infinitely many solutions

• one

• none

• infinitely many

• 8

How Many Solutions?

y = 6x + 1

y = 6x

• One

• None

• Infinite

Find the Number of of Solutions to a System of Equations.

• No Solution ∅

• IF the Slopes and the Y-Intercepts are the SAME

• One Solution

• IF the Slopes are the SAME by the Y-Intercepts are DIFFERENT

• Infinitely Many Solutions ∞

• IF the Slopes are DIFFERENT