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Published byEdwin Philipps Modified over 2 years ago

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

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

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

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

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y = 2x + 1

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

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

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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

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

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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

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

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Let’s Review Core Lesson

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Let’s Review Core Lesson

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

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Let’s Review Guided Practice

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Let’s Review Guided Practice

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

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

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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?

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

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

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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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