Do Now - Review Find the solution to the system of equations: x – y = 3 x + y = 5
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.
Intersecting Lines The point where the lines intersect is your solution. The solution of this graph is (1, 2) (1,2)
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.
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.
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.
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