3.1 Notes: Solving Systems of Equations

(4,4) is the solution to the system of the two equations! Ex#1 Graph the two lines on the same coordinate plane. What do you notice? The lines cross at (4, 4) (4,4) is the solution to the system of the two equations!

When you graph two lines that intersect, that is the solution to the system. The solution is an ordered pair that makes both equations true. Remember that we start to graph with the y-intercept, b, our beginning point and count our slope, m, moving point, to graph a line.

Ex. #2 Determine whether (3,5) is a solution of the system (x,y) y = 4x – 7 y = –x + 8 y = –x + 8 y = 4x – 7 5 = –(3) + 8 5 = 4(3) – 7 5 = 5 5 = 12 – 7 5 = 5 Yes, (3,5) is a solution to the system!

Ex. #3 Determine whether (-2,1) is a solution of the system (x,y) y = 2x + 5 3x + 2y = 3 3x + 2y = 3 y = 2x + 5 3(-2) + 2(1) = 3 1 = 2(-2) + 5 -6 + 2 = 3 1 = -4 + 5 -4 ≠ 3 1 = 1 NO! No, (-2,1) is NOT a solution to the system!

Ex#4 Solve by graphing. (2, 1)

Ex#5 Solve by graphing. x = –4 y = 4 (-2, 2)

Ex#6 Solve by graphing. Estimate the solution. 1 y = 2/5 or… (-4,2)

Ex#7 Solve by graphing. Estimate the solution. 4 y = 2 x = 4 y = -20/3 or… (4, 0)

x = -4/3 y = -4/5 7 x = -7/2 y = or… (-3, 1) Ex#8 Solve by graphing. Estimate the solution. x = -4/3 y = -4/5 7 x = -7/2 y = or… (-3, 1)

Ex#9 Solve by graphing. Estimate the solution. 1 y = -4 x = or… No Solution

Infinitely many solutions Ex#10 Solve by graphing. Estimate the solution. x = 5 y = -5/2 5 y = -5/2 x = Infinitely many solutions