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Can you look at a system of linear equations and tell how many solutions it has? For example: Could you tell that the equations y=2x +1 and y= 2x-7 have no solution? In this lesson you will learn to predict how many solutions a system of linear equations has by inspection. Let’s Review Let’s Review Slope Intercept Form of an Equation y = mx + b slope y-intercept Let’s Review Let’s Review Graphing a linear equation y = 2x + 1 slope y-intercept Let’s Review Let’s Review y = 2x + 1 A Common Let’s Review Mistake Assuming that all equations have one solution because those are the types of equations that are solved the most. CoreReview Lesson Let’s There are three types of solutions for systems of linear equations One None Infinitely Many CoreReview Lesson Let’s y = 2x + 1 y = 3x + 1 One point one solution 1 y= x-5 2 1 y= x-3 2 Parallel lines no solution y = 4x +4 y = 4(x+1) Same Line infinitely many solutions CoreReview Lesson Let’s Determine the number of solutions that the system has. y = -4(x+4) Slope: -4, y-intercept: -16 y = -4x-16 y = -4x-16 Slope: -4, y-intercept: -16 CoreReview Lesson Let’s Determine the number of solutions that the system has. y=x+1 Slope: 1, y-intercept: 1 1 y= x+1 2 1 Slope: , y-intercept: 1 2 CoreReview Lesson Let’s Determine the number of solutions that the system has. y = -5x + 1 Slope: -5, y-intercept: 1 y = -5x-2 Slope: -5, y-intercept: -2 In this lesson you learned to predict how many solutions a system of linear equations has by inspection. Guided Practice Let’s Review How many solutions does the system of linear equations have? y= -2x+1 y= -2x-2 Guided Practice Let’s Review How many solutions does the system of linear equations have? y= -3x+1 y= -2x-7 Guided Practice Let’s Review How many solutions does the system of linear equations have? y= -3(x+1) y= -3x-3 Extension Let’s ReviewActivities What are the possible number of solutions for a system of linear equations? Extension Let’s ReviewActivities Does the system of linear equations y=2x and y=2x+1 have infinitely many solutions? Explain your answer. Extension Let’s ReviewActivities Create a second equation for the following system of equations so that they have one solution, no solution, and infinitely many solutions. One solution y = 7x + 1 y= y = 7x + 1 y= y = 7x + 1 y= No solution Infinitely many solutions Quick Quiz Let’s Review How many solutions does the system of equations have? y=6(x+1) and y=6x+6 a) One b) None c) Infinitely Many How many solutions does the system of equations have? y=-3x and y=x+1 a) One b) None c) Infinitely Many