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Published byPhebe Ryan Modified over 7 years ago

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Do Now - Review Find the solution to the system of equations: x – y = 3 x + y = 5

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Systems of Equations - Definitions Systems of Equations – two or more equations together that offer a solution to a problem. On the graph, the solution to a system of linear equations is the point where the lines intersect. If when we graph the equations we see: Intersecting Lines – there is one solution to the system. Same Line – there are an infinite number of solutions. Parallel Lines – there is no solution to the system.

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

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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.

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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.

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Solving a System of Equations by Graphing There are 3 steps to solving a system using a graph. Step 1: Graph both equations. Step 2: Do the graphs intersect? Step 3: Check your solution. Graph using slope and y – intercept. Solve each equation for y first if necessary. This is the solution! (No or infinite solutions are possible.) Substitute the x and y values into both equations to verify the point is a solution to both equations.

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Back To The Do Now x – y = 3 x + y = 5

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Systems of Equations Ex. 1 Y = -x + 5 and y = x - 3 Solution (4,1)

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Ex. 2 y = -x + 5 and 2x + 2y = -8

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3. What is the solution of this system? 3x – y = 8 2y = 6x -16 1.(3, 1) 2.(4, 4) 3.No solution 4.Infinitely many solutions

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Ex. 4 x = 2 and 2x + y = 1

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7-1 Graphing Systems of Equations Using our Calculators 1.Enter the first equation into Y 1. 2.Enter the second equation into Y 2. 3. Hit GRAPH. 4. Use the INTERSECT option to find where the two graphs intersect (the answer). 2nd TRACE (CALC) #5 intersect Move spider close to the intersection. Hit ENTER 3 times. 5. Answer: x = 2.6 and y = 3.8 Solve the system: y = -2x + 9 and y = 3x - 4

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