<p> Name: ______Date: ______Math 11 Principles Section 5.3: The Number of Solutions for a System with Two lines</p><p>Let’s take a look at various possibilities.</p><p>Graph of Two Lines</p><p>Number of Solutions (intersections)</p><p>Consistent or Inconsistent</p><p>Compare the slopes of the two lines</p><p>Compare the Y intercepts of the 2 lines</p><p>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</p><p> 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</p><p>Consider the equation3x  5y  7 . Write a second equation such that the linear system will have…</p><p> a) no solution</p><p> b) only one solution</p><p> c) infinitely many solutions</p><p>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</p><p>Assignment: Page 321- 322 #1, 3, 4, 6 and 10b</p>