Solving Systems by Graphing
System of Linear Equations n Two or more linear equations graphed on the same grid or pertaining to the same situation.
Solution of a System Any point common to all the lines is a solution. n Any ordered pair that makes all the equations true is a solution of a system. n
Solving Systems by Graphing n n n Make sure both/all the equations are in the slopeintercept form (y = mx + b). Click on the moving calculator until you get a grid. Using either control g or clicking on the double arrows on the bottom left, enter the equations in f 1 and f 2 You may have to menu > 4 Window/Zoom> 5 Zoom Standard to get it centered. If you cannot see the point of intersection, zoom out (Menu > 4 Window/Zoom > 4 Zoom – Out).
Solving Systems by Graphing n n n Go to Menu > 6: Analyze Graph > 4: Intersection Lower Bound? Shows in the bottom left. Move the hand to the left of the point of intersection and click. Upper Bound? Shows in the bottom left. Move the hand to the right of the point of intersection and click. The ordered pair that shows near the point of intersection is the solution. Check by replacing the x and y with the appropriate numbers in both equations. The numbers should make BOTH equations true.
Example 1 n Find the solution of this system by graphing: y = 2 x – 3 ny = x – 1 n Answer: (2, 1) n Check. Replace x with 2 and y with 1 in both equations n 1 = 2(2) – 3 True n 1 = 2 – 1 True n
Example 2 n Solve y = x + 5 y = -4 x n Answer: (-1, 4) Check: Replace x with – 1 and y with 4 in the first and second equations 4 = -1 + 5 True 4 = -1 x – 4 True n
n The school band sells carnations on Valentine’s Day for $2 each. They buy the carnations from the florist for $0. 50 each with a $16 delivery charge.
Try these… n n n y=x– 3 y = -x – 1 y = -2 x – 1 y=x+5 y = 1/3 x - 3 y = -2 x + 4 n (1, -2) n (-2, 3) n (3, -2)
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