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System of quadratic-quadratic equations
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System of quadratic-quadratic equations
The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.
Basic Concepts: System of linear-quadratic equations, 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 two quadratic equations:
quadratic equation: y=ax2+bx+c
quadratic equation: y=dx2+ex+f
There are 4 cases to consider:case 1: 2 solutions case 2: 1 solution case 3: no solutions case 4: infinite solutions
- 1.Case 1: System with 2 Solutions
Solve the system, then verify the solutions graphically:
y=x2−6x+5
y=−2x2+9x−7
- 2.Case 2: System with 1 Solution
Solve the system, then verify the solutions graphically:
y=2x2+6x+7
y=−x2+4
- 3.Case 3: System with No Solutions
Solve the system, then verify the solutions graphically:
y=−x2+6x−10
y=2x2+6x+5
- 4.Case 4: System with Infinite Solutions
Solve the system, then verify the solutions graphically:
x2−4x−y+3=0
5y−5x2+20x−15=0
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17.
Simultaneous Equations
17.1
Determining number of solutions to linear equations
17.2
Solving simultaneous linear equations by graphing
17.3
Solving simultaneous linear equations by elimination
17.4
Solving simultaneous linear equations by substitution
17.5
Money related questions in linear equations
17.6
Unknown number related questions in linear equations
17.7
Distance and time related questions in linear equations
17.8
Rectangular shape related questions in linear equations
17.9
Simultaneous linear-quadratic equations
17.10
Simultaneous quadratic-quadratic equations
17.11
Solving 3 variable simultaneous equations by substitution
17.12
Solving 3 variable simultaneous equations by elimination
17.13
Solving 3 variable simultaneous equations with no solution, infinite solutions
17.14
Word problems relating 3 variable simultaneous equations
Don't just watch, practice makes perfect
Practice topics for Simultaneous Equations
17.1
Determining number of solutions to linear equations
17.3
Solving simultaneous linear equations by elimination
17.4
Solving simultaneous linear equations by substitution
17.5
Money related questions in linear equations
17.6
Unknown number related questions in linear equations
17.7
Distance and time related questions in linear equations
17.8
Rectangular shape related questions in linear equations
17.9
Simultaneous linear-quadratic equations
17.10
Simultaneous quadratic-quadratic equations