Section 5.3: the Number of Solutions for a System with Two Lines

Name: ______Date: ______Math 11 Principles Section 5.3: The Number of Solutions for a System with Two lines

Let’s take a look at various possibilities.

Graph of Two Lines

Number of Solutions (intersections)

Consistent or Inconsistent

Compare the slopes of the two lines

Compare the Y intercepts of the 2 lines

Determine if the system is consistent or inconsistent without trying to solve the system. a) y = 5x – 3 b) y = 3x + 2 c) y = -5x + 4 y = 5x + 4 y = 4x – 5 y = 5x + 4

d) y = 10x + 3 e) y + 2x = 7 f) -4x + 4y = 3 2.5y = 25x + 7.5 3y – x = 6 -x + y = 5 g) y – 4x = 3 h) 3x – 2y = 6 2y = 8x + 6 2x – 3y = -6

Consider the equation3x  5y  7 . Write a second equation such that the linear system will have…

a) no solution

b) only one solution

c) infinitely many solutions

Now let’s see what happens when you try to algebraically solve a system that has: a) No Solution b) Infinite number of solutions 2x + 3y = 24 2x + 3y = 24 2x + 3y = 12 6x + 9y = 72

Assignment: Page 321- 322 #1, 3, 4, 6 and 10b