13-2 Objective: Determine whether a system of equations has one solution, no solution, or an infinite number of solutions.

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Presentation transcript:

13-2 Objective: Determine whether a system of equations has one solution, no solution, or an infinite number of solutions

Guided questions What are the characteristics of a system of linear equations that have only one solution? What are the characteristics of a system of linear equations that have no solution. What are the characteristics of a system of linear equations that have an infinite number of solutions?

One solution As the name implies the two linear graphs have only one solution. This means they cross in only one place. Get both equations into slope-intercept form then graph. y=-2x+2 y=-3x+6

No solution Two linear graph that never cross are said to have “no solution”. y=-3x+6 y=-3x-3 When graphs have no solution they are parallel The slopes (m) are identical The y intercepts (b) are different m=-3 b= -3 and 6 2y+6x= 2

Infinite solutions An infinite number of solutions occur when one line lies on top of another. At any given point the lines cross The equations for both lines are the same; slopes and the y intercept are identical Y=-2x +3 2y+4x=6