Determine Solutions of Equations

-4(3x + 2) = 3(-4x + 5)

• No Solution

• One Solution

• Infinite Solution

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

• Same line

• Parallel lines

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

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two 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

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions