Ch 7: System of Equations E) Parallel & Same Lines Objective: To identify the number of solutions of a system of linear equations.

Intersection: Parallel:Coincidental Definitions Lines cross at one point only Lines never crossSame line – crosses at every point One solutionNo solution Infinitely many solutions x = ___, y = ____ False statementTrue Statement

y  –2 x  5 y  –2 x  1 Example 1 y  –2 x  5 y  –2 x  1 – ( ) 0 = False! No solution Graphing Elimination −

Example 2 -2x + y  3 −4x + 2y  6 2( ) = 0 True! Infinite solutions Graphing Elimination – 2x  y  3 – 4x  2y  6 LCM (x) = 4 −4x + 2y  6 Same Line – −−

Example 3 − x + 2y  3 4y = 2x + 8 2( ) = -2 False! No solution Graphing Elimination LCM (x) = 2 – Line up Like Terms −x + 2y  3 −2x + 4y = 6 −2x + 4y = 8 −−

Example 4 Graphing 3y = x + 6 2x – 6y  -12 3y = x + 6 2x – 6y = -12 2( ) = 0 True! Infinite solutions Elimination LCM (x) = 2 + Line up Like Terms -x + 3y  6 2x – 6y = x + 6y = 12

Classwork y = x + 4 y = x – 3 No solution 1) x + y = -3 -2x – 2y = 6 2) Infinite solutions Solve each system by Graphing

9x – 2y = 6 -9x + 2y = -6 Infinite solutions 3) 4x + 6y = -2 -4x – 6y = 12 4) 6x + 7y = 6 6x + 7y = -7 5)4x + 8y = -12 8x + 16y = -24 6) No solution Infinite solutions Solve each system using Elimination