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What happens if we graph a system of equations and the lines are parallel?

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Presentation on theme: "What happens if we graph a system of equations and the lines are parallel?"— Presentation transcript:

1 What happens if we graph a system of equations and the lines are parallel?

2 In this lesson you will determine if a system of two linear equations in two variables has no solution by graphing.

3 Let’s Review Slope Intercept Form of an Equation y = mx + b slopey-intercept

4 Graphing a linear equation y = 2x + 1 slopey-intercept

5 y = 2x + 1

6 A Common Mistake Thinking that all systems of equations must have one solution

7 Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = 2x y - 4 = 2x + 4 = + 4 y = 2x + 4

8 Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = 2x y = 2x+4 Slope: 2, y-intercept: 0 Slope: 2, y-intercept: 4

9 Let’s Review Core Lesson y = 2x y = 2x+4

10 Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. -x + 2y = 02y – x = - 2 +x = +x 2y = x 2 = 2 +x = +x 2y = x = 2

11 Let’s Review Core Lesson Graph the system of linear equations. Determine their solution.

12 Let’s Review Core Lesson

13 Let’s Review Core Lesson

14 In this lesson you learned to determine if a system of two linear equations in two variables has no solution by graphing.

15 Let’s Review Guided Practice

16 Let’s Review Guided Practice

17 Let’s Review Guided Practice Find the solution for the system of linear equations y=3x and y=3x-2 by graphing.

18 Let’s Review Guided Practice y=3x y= 3x-2

19 Let’s Review Extension Activities When we solve the systems of equations y=2x and y=2x +1, what is our solution? What does it mean?

20 Let’s Review Extension Activities How many solutions does the system of equations y=3x+1 and y=3x-2 have? Why?

21 Let’s Review Extension Activities Create a system of linear equations that have no solutions.

22 Let’s Review Quick Quiz The solution for the system of linear equations y=2x+1 and y=2x-3 is? a) (-1,1) b) (1,-1) c)(-1,-1) d) no solution The solution for the system of linear equations y=-x+6 and y=-x-2 is? a) (2,-4) b) (-2,4) c) (-2,-4) d) no solution


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