# Solve Systems by Graphing

Do Now: Journal Describe the steps that you must take to accurately graph an equation. What are some of the typical errors that students may make? Objective The student will be able to: solve systems of equations by graphing. December 2, 2014 What is a system of equations? A

system of equations is when you have two or more equations using the same variables. The solution to the system is the point that satisfies ALL of the equations. This point will be an ordered pair. When graphing, you will encounter three possibilities. Intersecting Lines The

point where the lines intersect is your solution. The solution of this graph is (1, 2) (1,2) Parallel Lines These lines never

intersect! Since the lines never cross, there is NO SOLUTION! Parallel lines have the same slope with different y-intercepts. 2 Slope = = 2 1 y-intercept = 2

y-intercept = -1 Coinciding Lines These lines are the same! Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! Coinciding lines have the same slope and

y-intercepts. 2 Slope = = 2 1 y-intercept = -1 What is the solution of the system graphed below? 1. 2.

3. 4. (2, -2) (-2, 2) No solution Infinitely many solutions 1) Find the solution to the following system: 2x + y = 4 x-y=2

Graph both equations. You may graph using x- and y-intercepts 2x + y = 4 (0, 4) and (2, 0) xy=2 (0, -2) and (2, 0) Graph the ordered pairs. Graph the equations.

y= 4 x-y=2 (0, -2) and (2, 0) + 2x 2x + y = 4 (0, 4) and (2, 0) x

y= Where do the lines intersect? (2, 0) 2 Check your answer! To check your answer, plug the point back into both equations.

2x + y = 4 2(2) + (0) = 4 x-y=2 (2) (0) = 2 Nice joblets try another! 2) Find the solution to the following system: y = 2x 3 -2x + y = 1 Graph both equations. Put both equations

in slope-intercept or standard form. Ill do slope-intercept form on this one! y = 2x 3 y = 2x + 1 Graph using slope and y-intercept Graph the equations. y = 2x 3 m = 2 and b = -3 y = 2x + 1 m = 2 and b = 1 Where do the lines intersect?

No solution! Notice that the slopes are the same with different y-intercepts. If you recognize this early, you dont have to graph them! Check your answer! Not a lot to checkJust make sure you set up your equations correctly. I double-checked it and I did it right

What is the solution of this system? 3x y = 8 2y = 6x -16 (3, 1) 2. (4, 4) 3. No solution 4. Infinitely many solutions 1. What x coordinate will be a solution to f(x) and g(x)? f(x) = - 4x + 5

g(x) = 3x 9 Step 1: Set functions equal to each other -4x + 5 = 3x 9 Step 2: Solve as an equation with variables on both sides 5 = 7x 9 14 = 7x 2=x Step 3: Identify the x coordinate that will be the solution for both functions. The x coordinate of 2 will be a solution for both f(x) and g(x). Try this one: f(x) = -x + 4

g(x) = (-2x + 10) Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Graph using slope and y intercept or x- and y-intercepts. Be sure to use a ruler and graph paper!

Step 2: Do the graphs intersect? This is the solution! LABEL the solution! Step 3: Check your solution. Substitute the x and y values into both equations to verify the point is a solution to both equations.

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