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Warm ups What is the slope and y intercept? 1 y x3 2 2x 3 y 6 y 1 2( x 5) 8.1 Graphing Systems of Equations Objective: To solve systems of equations by graphing. System of Linear Equations: System of Linear Equations: Two or more linear equations. A solution to the system of linear equations is any ordered pair that makes BOTH equations true. Three Types of Solutions: Intersection is Solution One Solution Different slope Different y-intercept “Intersect at one point” No Solution Same slope Different y-intercept “Run parallel Never intersect” Infinite Solutions Same slope Same y-intercept “Same line Intersect infinitely” Examples: Solve each system by graphing. 1) y = –x + 1 y = 2x + 4 y = –x + 1 y = 2x + 4 Slope: -1 Slope: 2 Y-int: (0, 1) Y-int: (0, 4) Different slope Different y-intercept “Intersect at one point” The solution of the system is: (-1, 2) x = –1, y = 2 2) x + y = 1 y = –x + 3 x+y=1 –x –x y=-x+1 y = –x + 3 Slope: -1 Y-int: (0, 3) Slope: –1 Y-int: (0, 1) Same slope Different y-intercept “Run parallel Never intersect” The solution of the system is: no solution 3) x – 2y = 4 2x – 4y = 8 x – 2y = 4 –x –x –2y = –x + 4 –2 –2 –2 y =½x–2 2x – 4y = 8 –2x –2x –4y = –2x + 8 –4 –4 –4 Y=½x–2 Slope: ½ Slope: ½ Y-int: (0, –2) Y-int: (0, –2) Same slope Same y-intercept “Same line Intersect infinitely” The solution of the system is: infinite solutions Try with a Partner: 4) y = 3x – 3 x+y=1 y = 3x – 3 Slope: 3 x+y=1 –x –x y = –x + 1 Y-int: (0, –3 ) Slope: –1 Y-int: (0, 1) Different slope Different y-intercept “Intersect at one point” The solution of the system is: (1, 0) x = 1, y = 0 Summarize: HOW MANY ANSWERS? Number of Solutions 1 (Ordered Pair) Slope Y-Intercept Different Same Different 0 (No Solution) ∞ (Infinitely Many) Same Different Same Same TRY ON OWN Answer the four multiple choice questions on the elmo. Speaker and Scribe Review 1 1 3 x x 2 5 10 3x 2 x 4 3 x 33 8 x 3 x 88 Review 5x 1 1 8 2 2 2 x 48 5 x x5 8 6 3 x 5 x 20 x 20 Review 5 x 10 5 6 x4 10 3x 6 x 8 x6 6 x 2 5( x 3) x NOsolution Write in STANDARD (1, 2)(1,8) 5x y 3 1 ( 4, 6) m 2 x 2y 8 Determine Value of r. 5 (4, r )( r , 2) m r7 3 3 (3, r )(r ,5)m 5 r 8 Homework 8.1 Graphing Systems of Linear Equations (2 sides)