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- Simultaneous Equations
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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13.
Simultaneous Equations
13.1
Determining number of solutions to linear equations
13.2
Solving simultaneous linear equations by graphing
13.3
Solving simultaneous linear equations by elimination
13.4
Solving simultaneous linear equations by substitution
13.5
Money related questions in linear equations
13.6
Unknown number related questions in linear equations
13.7
Distance and time related questions in linear equations
13.8
Rectangular shape related questions in linear equations
13.9
Simultaneous linear equations
13.10
Simultaneous linear-quadratic equations
13.11
Simultaneous quadratic-quadratic equations
Don't just watch, practice makes perfect
Practice topics for Simultaneous Equations
13.1
Determining number of solutions to linear equations
13.3
Solving simultaneous linear equations by elimination
13.4
Solving simultaneous linear equations by substitution
13.5
Money related questions in linear equations
13.6
Unknown number related questions in linear equations
13.7
Distance and time related questions in linear equations
13.8
Rectangular shape related questions in linear equations
13.10
Simultaneous linear-quadratic equations
13.11
Simultaneous quadratic-quadratic equations