1. SYSTEM OF LINEAR EQUATIONS
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2. LINEAR EQUATION IN 2 VARIABLES
Two points determine a line, so just need to plot 2 points to draw the line.
We may assign any other value to x or y and solve for the value of the other variable using the equation.
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3. All points lying on this line will satisfy the equation 3x+4y-12=0.
y-intercept
x-intercept
All points lying on this line will satisfy the equation 3x+4y-12=0.
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4. x-intercept is the x coordinate of the point of intersection of the graph (line) with the x-axis ( y = 0 ).
y-intercept is the y coordinate of the point of intersection of the graph (line) with the y-axis ( x = 0 ).
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5. Special Cases: k
y = 0
x-axis
IkI
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6. Special Cases:
x = 0
y-axis
IkI k
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7. System of 2 Linear Equations in 2 Variables
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8. System of 2 Linear Equations in 2 Variables
Every point on each of the lines is a solution.
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9. System of 2 Linear Equations in 2 Variables
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10. System of 2 Linear Equations in 2 Variables
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11. Solve the following systems of linear equations:
Consistent independent system:
One solution
Graphically: intersecting lines
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12. one point of intersection
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13. Inconsistent system : NO solution
Graphically: parallel lines
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14. Consistent dependent system: Infinitely many solutions
Graphically: coincident lines
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15. Consistent independent system: one solution
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18. System of 3 Linear Equations in 3 Variables
Elimination and substitution methods can be utilized to solve system of 3 linear equations in 3 variables.
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19. Solve the following systems of 3 Linear Equations in 3 Variables:
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21. Solve the following systems of 3 Linear Equations in 3 Variables:
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23. Solve the following systems of 3 Linear Equations in 3 Variables:
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26. System of Linear and Non-linear Equations in 2 Variables
Solve the following systems of non-linear equations:
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27. So we don’t have real number solution for this system.
System of Linear and Non-linear Equations in 2 Variables
Solve the following systems of non-linear equations:
Note that we have complex numbers as coordinates. This means that algebraically we have solutions (complex number solutions) to this system but graphically there will be NO POINT OF INTERSECTION for the 2 given curves on the Cartesian Plane.
So we don’t have real number solution for this system.
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29. quadratic equation in one variable
linear
quadratic
quadratic equation in one variable
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