Graph to estimate the solution of the linear system. More notes to copy in my notebook!ĩ Graph to estimate the solution of the linear system 4) Check whether the coordinate gives a solution by substituting it into each equation of the original linear system. 3) Estimate the coordinate of the point of intersection. 2) Graph both equations in the same coordinate plane. Solving A Linear System Using Graph–and–Check 1) Write each equation in a form that is easy to graph. solution If the ordered pair makes each equation true, it is the solution of the system of linear equations. not a solution Example 2 Is the ordered pair (-1,2) a solution of the given system? Show your work. Point of intersection (2,–1) (x,y)ħ Example 1 Is the ordered pair (0,1) a solution of the given systemĮxample 1 Is the ordered pair (0,1) a solution of the given system? Show your work. The ordered pair (2,–1) makes each equation true, therefore it is the solution of the system of linear equations.Then check your solution algebraically using substitution. Use the graph to find the solution of the linear system. y x Same lines – infinitely many solutions.Ħ Use the graph to find the solution of the linear system If the graphs are the same line then there are infinitely many solutions. X Parallel lines will never intersect thus no solution.ĥ Same lines – infinitely many solutions. Intersecting lines – exactly one solution!Ĥ If the graphs are parallel, the system of equations has no solution.Notes to copy in my notebook!ģ When there is one solution it is the point where the graph of each equation intersect. A system of two linear equations can have no solution, one solution, or infinitely many solutions. The ordered pair solution is the point of intersection on the graph of the equations. ![]() Here is an example: x + y = Equation 1 2x – 3y = Equation 2 A solution of a linear system in two variables is an ordered pair that makes each equation a true statement. Two or more linear equations in the same variable form a system of linear equations, or simply a linear system. ![]() Presentation on theme: "5-1 Graphing Systems of Equations"- Presentation transcript:Īlgebra Glencoe McGraw-Hill Linda Stamper
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