Presentation on theme: "Solving Systems of Linear Equations Graphically"— Presentation transcript:
1 Solving Systems of Linear Equations Graphically 9.1Solving Systems of Linear Equations Graphically1. Determine whether an ordered pair is a solution for a system of equations.2. Solve a system of linear equations graphically.3. Classify systems of linear equations in two unknowns.
2 System of equations: A group of two or more equations. Solution for a system of equations: An ordered pair that makes all equations in the system true.
3 To Check a Solution to a System of Equations 1. Replace each variable in each equation with its corresponding value.2. Verify that each equation is true.
4 Determine whether the ordered pair (3, 4) is a solution to the system of equations. y = 3x – 24 = 3(3) – 24 = 7FalseBecause (3, 4) does not satisfy both equations, it is not a solution to the system of equations.x + y = 73 + 4 = 77 = 7True
5 Determine whether the ordered pair (3, 2) is a solution to the system of equations. x + y = 7 y = 3x – 23 + 2 = = 3(3) – 21 = 7 2 = 11False FalseBecause (3, 2) does not satisfy both equations, it is not a solution for the system.
8 (Not the same as all real numbers.) A system of two linear equations in two variables can have one solution, no solution, or an infinite number of solutions.The graphs intersect at a single point. There is one solution.The equations have the same slope, the graphs are parallel. There is no solution.The graphs are identical. There are an infinite number of solutions.(Not the same as all real numbers.)
9 Solving Systems of Equations Graphically 1. Graph each equation.a. If the lines intersect at a single point, then the coordinates of that point form the solution.b. If the lines are parallel, there is no solution.c. If the lines are identical, there are an infinitenumber of solutions. They are the coordinatesof all the points on that line.2. Check your solution.
10 Solve the system of equations graphically. Graph each equation:y = 2 – xy = -x (0,2) m = -12x + 4y =12(0,3) (6,0) m = -½Intersection:(2, 4)2x + 4y = 12y = 2 – xThe solution is (-2,4).
11 Solve the system of equations graphically. The slopes are the same, so the lines are parallel. The system has no solution
12 Solve the system of equations graphically. The equations are identical. All ordered pairs along the line are solutions.