Solutions to Systems of Equations

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

How can you tell if a point is a solution to a system?

• It makes the first equation true.
• The (x,y) coordinates satisfy both equations
• It makes logical sense
• It makes neither equation negative

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

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

What is the solution to the system?

• (-1, 3)

• (-3, 1)

• (3, -1)

• (-3, -1)

How many solutions will this system have?

• One
• Two
• No Solution
• 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

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

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.