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System of linear-quadratic equations
- Intro Lesson2:34
- Lesson: 1a10:28
- Lesson: 1b3:19
- Lesson: 2a6:50
- Lesson: 2b6:53
- Lesson: 3a5:46
- Lesson: 3b3:20
System of linear-quadratic equations
The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.
Basic Concepts: Solving systems of linear equations by graphing, Solving systems of linear equations by elimination, Solving systems of linear equations by substitution, Solving quadratic equations by factoring, Solving quadratic equations using the quadratic formula
Related Concepts: Graphing linear inequalities in two variables, Graphing systems of linear inequalities, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities
Lessons
- Introduction• The solutions to a system of equations are the points of intersection of the graphs.
• For a system consisting of a linear equation and a quadratic equation:
linear equation: y=mx+b
quadratic equation: y=ax2+bx+c
There are 3 cases to consider:
case 1: 2 solutions case 2: 1 solution case 3: no solutions
- 1.Case 1: System with 2 Solutionsa)Solve the system:
y=−x+1
y=x2+x−2b)Verify the solutions graphically - 2.Case 2: System with 1 Solutiona)Solve the system:
2x−y=8
y=x2−4x+1b)Verify the solutions graphically - 3.Case 3: System with No Solutionsa)Solve the system:
10x+5y+15=0
y=x2−4x+2b)Verify the solutions graphically
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11.
Simultaneous Equations (Advance)
11.1
Simultaneous linear equations
11.2
Simultaneous linear-quadratic equations
11.3
Simultaneous quadratic-quadratic equations
11.4
Solving 3 variable simultaneous equations by substitution
11.5
Solving 3 variable simultaneous equations by elimination
11.6
Solving 3 variable simultaneous equations with no or infinite solutions
11.7
Word problems relating 3 variable simultaneous equations