Chapter 6 Vocabulary (6-1) 1.) System of linear equations 2.) Solution of a system of linear equations 3.) consistent 4.) independent 5.) dependent 6.) inconsistent

SOLVING SYSTEMS BY GRAPHING ALGEBRA 1 6-1

SYSTEMS OF LINEAR EQUATIONS ARE TWO EQUATIONS THAT HAVE 3 POSSIBLE SOLUTIONS.

THREE POSSIBLE SOLUTIONS FOR SYSTEMS OF EQ.’S One Solution is the intersection point of the two equations represented as an ordered pair (x,y) which is consistent & independent. No Solution occurs when there is no intersection due to the fact that they are parallel lines which are inconsistent. Infinitely Many Solutions occurs when both equations are the same line consistent & dependent.

GRAPHING SYSTEMS OF EQ.’S Graph each equation on one coordinate plane using the T-chart method or the slope-intercept method. The solution should be apparent.

Ex. 1 -Use the graph to solve the system of linear equations. y= 3x – 12 y = -2x + 3

Example 2 Graph y= -x + 5 y = x - 3

Graph Ex. 3 y=6 x=-2

Example 4 Graph y= x + 2 y= x - 3

Example 5 3x + y = 3 2y = -6x + 6

Assignment

Checking the Intersection Point Ex. 1 - Decide whether the ordered pair is a solution of the system of linear equations. (-1, 0) -2x + y =2 x + y = -1