<p> Solve Special Types of Linear Systems</p><p>Inconsistent System a linear system with no solution. The graph of an inconsistent system resembles 2 parallel lines.</p><p>Consistent Dependent System a linear system with infinitely many solutions. The graph of the systems is the same line.</p><p>A linear system with no solution: Example: show that the linear system has no solution.</p><p>3x+2y=10 3x+2y=2</p><p>Put both equations in slope-intercept form Graph the linear systems- the linear are parallel because they have the same slope but different y-intercepts. Parallel lines do not intersect, so the system has no solution.</p><p>A linear system with infinitely many solutions Example: show that the linear system has infinitely many solutions.</p><p> x-2y=-4 1 y = x + 2 2 Put the firs linear system in slope-intercept form.</p><p>You will see that the linear equations are identical so they are the same line. So the linear system has infinitely many solutions.</p><p>Help in identifying the number of solutions.</p><p>Number of Solutions Soles and y-intercepts One Solution Different Slopes No Solution Same Slope Different y-intercepts Infinitely Many Solutions Same Slope Same y-intercept Identifying the Number of Solutions</p><p>Without solving the linear system, tell whether the linear system has one solution, no solution, or infinitely many solutions. a) 5x+y=-2 b) 6x+2y=3 -10x-2y=4 6x+2y=-5 Solution: Solution: Get both equations in slope-intercept Get both equations in slope-intercept form: form: Y=-5x-2 3 y = - 3x + Y=-5x-2 2 Because the lines have the same slope 5 y = - 3x - and the same y-intercept, the system has 2 infinitely many solutions. Because the lines have the same slope </p><p> but different y-intercepts, the system has no solution. </p>