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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Graphing Systems of Equations

  • A system of equations is two equations in two variables. A solution consists of values for each unknown that satisfy both equations.
  • A system can have one, infinite, or no solutions.
  • The system is called independent if it has one solution. In this case, the graphs of the two equations intersect at one point.
  • It is called dependent if it has infinitely many solutions. In this case, the graphs are the same line.
  • It is called inconsistent if it has no solution. In this case, the graphs are parallel.
  • You can solve a system by graphing. Always check your solutions to be sure you have read the graph accurately.
  • Use the method of graphing when you are willing to settle for an estimate for the solution.

Graphing Systems of Equations

Solving the system by graphing
x + 2y = 35x + y = 5
  • Find two points for each equation by setting x = 0 then y = 0
  • x + 2y = 3 → ( 0,[1/2] ),( 3,0 )
  • 5x + y = 5 → ( 5.0, ),( 5,0 )
Graph to find intersection

(7, - 2)
Solving the system by graphing
y − x = 42y − x = 3
  • Find two points for each equation by setting x = 0 then y = 0
  • y − x = 4 → ( 0,4 ),( − 4,0 )
  • 2y − x = 3 → ( 0,[3/2] ),( − [3/2],0 )
Graph to find intersection

( - 5, - 1)
Solving the system by graphing
− x + 4y = 20y − 3x = 16
  • Find two points for each equation by setting x = 0 then y = 0
  • x + 4y = 20 → ( 0,5 ),( − 20,0 )
  • y − 3x = 16 → ( 0, − [16/3] ),( 16,0 )
Graph to find intersection

( - 4,4)
Solving the system by graphing
− x + 6y = 12y + x = 9
  • Find two points for each equation by setting x = 0 then y = 0
  • − x + 6y = 12 → ( 0, − 12 ),( 2,0 )
  • y + x = 9 → ( 9,0 ),( 0,9 )
Graph to find intersection

(6,3)
Solving the system by graphing
x + 2y = 16x + y = 8
  • Find two points for each equation by setting x = 0 then y = 0
  • x + 2y = 16 → ( 0,8 ),( 16,0 )
  • x − y = 8 → ( 8,0 ),( 0,8 )
Graph to find intersection

(0,8)
Solving the system by graphing
x + 2y = − 123y − x = 6
  • Find two points for each equation by setting x = 0 then y = 0
  • x + 2y = − 12 → ( − 12,0 ),( 0, − 6 )
  • 3y − x = 6 → ( − 6,0 ),( 0,2 )
Graph to find intersection

( - 6,0)
Solving the system by graphing
x + y = 5y = − 3
  • Find two points for each equation by setting x = 0 then y = 0
  • x + y = 5 → ( 5,0 ),( 0,5 )
  • y = − 3 → ( 0, − 3 ),( 0, − 3 )
Graph to find intersection

(8, - 3)
Solving the system by graphing
y − 3x = 2− 9x + 3y = 6
  • Find two points for each equation by setting x = 0 then y = 0
  • x + y = 5 → ( − [3/2],0 ),( 0,2 )
  • y = − 3 → ( − [3/2],0 ),( 0,2 )
Graph to find intersection

Infinite solutions
Solving the system by graphing
2y − x = − 8y − x = − 3
  • Find two points for each equation by setting x = 0 then y = 0
  • 2y − x = − 8 → ( 0, − 4 ),( 8,0 )
  • − y + x = 3 → ( 3,0 ),( 0, − 3 )
Graph to find intersection

( - 2, - 5)
Solving the system by graphing
y + 2x = 5x + [y/2] = 2
  • Find two points for each equation by setting x = 0 then y = 0
  • y + 2x = 5 → ( 0,5 ),( [5/2],0 )
  • x + [y/2] = 2 → ( 2,0 ),( 0,4 )
Graph to find intersection

No solutions

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Graphing Systems of Equations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Systems of Equations 0:10
    • Definition
    • Example
    • Solution
  • Solving by Graphing 1:23
    • Points of Intersection
    • Example
  • Number of Solutions 3:09
    • Independent
    • Dependent
    • Inconsistent
  • Example 1: Solve by Graphing 5:45
  • Example 2: Solve by Graphing 9:50
  • Example 3: Solve by Graphing 14:17
  • Example 4: Solve by Graphing 18:03