Warm ups What is the slope and y intercept?

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 Infinite Solutions No Solution Different slope Different y-intercept “Intersect at one point” Same slope Different y-intercept “Run parallel  Never intersect” 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 Slope: -1 Y-int: (0, 1) y = 2x + 4 Slope: 2 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 y = –x + 3 –x –x y = - x + 1 Slope: -1 Y-int: (0, 1) y = –x + 3 Slope: –1 Y-int: (0, 3) Same slope Different y-intercept “Run parallel  Never intersect” The solution of the system is: no solution

“Same line  Intersect infinitely” 3) x – 2y = 4 2x – 4y = 8 x – 2y = 4 –x –x –2y = –x + 4 –2 –2 –2 y = ½ x – 2 Slope: ½ Y-int: (0, –2) 2x – 4y = 8 –2x –2x –4y = –2x + 8 –4 –4 –4 Y = ½ x – 2 Slope: ½ Y-int: (0, –2) The solution of the system is: infinite solutions Same slope Same y-intercept “Same line  Intersect infinitely”

Try with a Partner: 4) y = 3x – 3 x + y = 1 y = 3x – 3 x + y = 1 –x –x Slope: 3 Y-int: (0, –3 ) x + y = 1 –x –x y = –x + 1 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 Slope Y-Intercept 1 (Ordered Pair) Different Same (No Solution) ∞ (Infinitely Many)

TRY ON OWN Answer the four multiple choice questions on the elmo.

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Determine Value of r.

Homework 8.1 Graphing Systems of Linear Equations (2 sides)