Systems of Equations Basics

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)

What is the solution?

• (6, 3)

• (3, 6)

• (-6, 3)

• No solution

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

What is the Solution to this system?

• (2,-2)

• (-2,2)

• All Real Numbers

• No 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

This system has _____ solutions

(Hint: Both lines are graphed over each other)

• 1

• 2

• Infinitely Many

• no

NO CALC: What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution

• (6, -2)

NO CALC: What is the solution to this system?

• (-2, -2)

• (2, -2)

• (-2,2)

• (2, 2)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3x + 2y = 315

  2x + 4y = 450

• 3x + 2y = 450

  2x + 4y = 315

• 2x + 2y = 315

  3x + 4y = 450

What are the solution(s) to the systems shown?

• (-2,0) (2,0)

• (-2,0) (1,-3)

• (0,-2) (-3,1)

• (0,-4) (0,-2)