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Bellwork 11/12/18. Pg. 228. Chapter 3 Lesson 7 Solving Systems by graphing. Objective. The student will be able to: solve systems of equations by graphing. What is a system of equations?. A system of equations is when you have two or more equations using the same variables.
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Bellwork 11/12/18 Pg. 228
Objective The student will be able to: solve systems of equations by graphing.
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 BOTH equations. This point will be an ordered pair (x,y) telling where the two lines intersect aka cross.
Stop & Think! • How can you use what you already know about equations in slope-intercept form to find the point these two lines have in common?
What conjecture can you make about the solution to the system shown? • The point (x,y) where the lines intersect is your solution aka ANSWER! • The solution of this graph is (1, 2) (1,2)
Make an Inference • What inference can you make about two lines with the same slope? Ex. )
Parallel Lines • These lines never intersect! • Since the lines never cross, there is NO SOLUTION! • Parallel lines have the same slope but different y-intercepts.
Identical Lines touch EVERYWHERE! • These lines are the same! • Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS! • They have the exact same slope and y-intercept.
What is the solution of the system graphed below? • (2, -2) • (-2, 2) • No solution • Infinitely many solutions
1.) Graph both equations to find the solution (x,y) y = -2x+2 y = 2x-2
2.) Graph the equations to find the solution. y = -2x+4 y = x - 2
3.) Find the solution to the following system by graphing: y = 2x – 3 y = 2x+1
Explain why in a system with no solution the lines never touch/cross.
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 don’t have to graph them!
4.) What is the solution of this system? y = 3x+8 y = 3x+8 • (3, 1) • (4, 4) • No solution • Infinitely many solutions
5.) evaluate the solution to the following system of equations by graphing. 6x - y= 8 -2x +y = 4
6.) evaluate the solution to the following system of equations by graphing 3x + y = 6 -2x +2y= 12
Solving a system of equations by graphing. Let's summarize! There are 3 steps to solving a system using a graph. Graph using slope and y – intercept or x- and y-intercepts. Be sure to use a ruler and graph paper! Step 1: Graph both equations. This is the solution! LABEL the solution! Step 2: Do the graphs intersect? Substitute the x and y values into both equations to verify the point is a solution to both equations. Step 3: Check your solution.
INDEPENDENT PRACTICE Textbook page 239 (1-6)
Exit Ticket 1.) What is the solution to the system? 2.) Describe the 3 different types of solutions and what they look like on a graph.