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Warm Up

Warm Up. Graph the lines on the same grid and identify the point where they meet. y=2x-2 y=x+1. Objective. You 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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Warm Up

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  1. Warm Up Graph the lines on the same grid and identify the point where they meet. y=2x-2 y=x+1

  2. Objective You will be able to: solve systems of equations by graphing.

  3. 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 (x,y). • When graphing, you will encounter three possibilities.

  4. Intersecting Lines • The point where the lines intersect is your solution. • The solution of this graph is (1, 2) (1,2)

  5. 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.

  6. 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.

  7. What is the solution of the system graphed below? • (2, -2) • (-2, 2) • No solution • Infinitely many solutions

  8. Example 1: Solve this system y= -x +7 y= x -1 All we need to do is graph the two lines and see where they intersect.

  9. Example 1 Cont… y= -x +7 y= x -1

  10. Example 1 Cont… The last step is to check your answer. You do this by plugging the solution point (x,y) into each equation and checking to see if it works.

  11. Example 1 cont… Our equations are: y= -x +7 y= x -1 And our solution is (4,3) So: 3 = - 4 +7 And 3 = 4-1 It works! So we know we did it right and (4,3) is in fact our solution!

  12. Example 2: You try! y= 4x – 1 y= -x +4

  13. Example 2 cont… Solution: (1,3)

  14. 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.

  15. Homework • http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Systems%20of%20Equations%20Graphing.pdf • Problems 1-4

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