ObjectiveThe student will be able to:solve systems of equations by graphing.
What is a system of equations?A system of equations is when you havetwo or more equations using the samevariables.The solution to the system is the pointthat satisfies ALL of the equations. Thispoint will be an ordered pair.When graphing, you will encounter threepossibilities.
Intersecting LinesThe point where the linesintersect is your solution.The solution of this graphis (1, 2)(1,2)
Parallel Lines These lines neverintersect! Since the lines nevercross, there isNO SOLUTION! Parallel lines have thesame slope with differenty-intercepts.2Slope = = 21y-intercept = 2y-intercept = -1
Coinciding Lines These lines are the same! Since the lines are on topof each other, there areINFINITELY MANYSOLUTIONS! Coinciding lines have thesame slope andy-intercepts.2Slope = = 21y-intercept = -1
What is the solution of the systemgraphed below?1. (2, -2)2. (-2, 2)3. No solution4. Infinitely many solutions
1) Find the solution to the followingsystem:2x + y = 4x - y = 2Graph both equations. I will graph usingx- and y-intercepts (plug in zeros).Graph the ordered pairs.2x + y = 4(0, 4) and (2, 0)x – y = 2(0, -2) and (2, 0)
Graph the equations.2x + y = 4(0, 4) and (2, 0)x - y = 2(0, -2) and (2, 0)Where do the lines intersect?(2, 0)2x+y=4x – y =2
Check your answer!To check your answer, plugthe point back into bothequations.2x + y = 42(2) + (0) = 4x - y = 2(2) – (0) = 2 Nice job…let’s try another!
2) Find the solution to the followingsystem:y = 2x – 3-2x + y = 1Graph both equations. Put both equationsin slope-intercept or standard form. I’ll doslope-intercept form on this one!y = 2x – 3y = 2x + 1Graph using slope and y-intercept
Graph the equations.y = 2x – 3m = 2 and b = -3y = 2x + 1m = 2 and b = 1Where do the lines intersect?No solution!Notice that the slopes are the same with differenty-intercepts. If you recognize this early, you don’thave to graph them!
Check your answer!Not a lot to check…Justmake sure you set upyour equations correctly.I double-checked it and Idid it right…
What is the solution of this system?3x – y = 82y = 6x -161. (3, 1)2. (4, 4)3. No solution4. Infinitely many solutions
Solving a system of equations by graphing.Lets summarize! There are 3 steps tosolving 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 – interceptor x- and y-intercepts. Be sure to usea ruler and graph paper!This is the solution! LABEL thesolution!Substitute the x and y values intoboth equations to verify the point isa solution to both equations.