Graphing Systems of Equations

What is a System? A system refers to two lines graphed on the same coordinate plane. The solution to a system is the point or points that the two lines have in common.

Example System y = -x + 4 & y = x - 2 1) Graph both equations on the same plane. A) y = -x + 4 y-int = 4 slope = -1/1

Example System (continued) y = -x + 4 & y = x - 2 1) Graph both equations on the same plane. B) y = x - 2 y-int = -2 slope = 1/1

Example System (continued) y = -x + 4 & y = x - 2 2) If the lines intersect (cross), the solution is the intersection point. What is this point? (3, 1)

Example System (continued) y = -x + 4 & y = x - 2 3) To check the solution, substitute the x and y values of the point into the x and y variables of the equations. Both equations should be balanced. (3, 1) A) y = -x + 4 1 = -(3) + 4 1 = 1 √

Example System (continued) y = -x + 4 & y = x - 2 3) To check the solution, substitute the x and y values of the point into the x and y variables of the equations. Both equations should be balanced. (3, 1) B) y = x - 2 1 = 3 - 2 1 = 1 √

Example #2 y = -x - 2 & y = 3x + 6 1) Graph both equations on the same plane. A) y = -x + 2 y-int = 2 slope = -1/1

Example #2 (continued) y = -x - 2 & y = 3x + 6 1) Graph both equations on the same plane. B) y = 3x + 6 y-int = 6 slope = 3/1

Example #2 (continued) (-2, 0) y = -x - 2 & y = 3x + 6 2) What is the solution? (-2, 0) 3) Check it: A) y = -x - 2 0 = -(-2)- 2 0 = 2 - 2 0 = 0 √ B) y = 3x + 6 0 = 3(-2)+ 6 0 = (-6) + 6 0 = 0 √