SYSTEM OF LINEAR EQUATIONS S.Y.Tan

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. S.Y.Tan

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. S.Y.Tan

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 ). S.Y.Tan

Special Cases: k y = 0 x-axis IkI S.Y.Tan

Special Cases: x = 0 y-axis IkI k S.Y.Tan

System of 2 Linear Equations in 2 Variables S.Y.Tan

System of 2 Linear Equations in 2 Variables Every point on each of the lines is a solution. S.Y.Tan

System of 2 Linear Equations in 2 Variables S.Y.Tan

System of 2 Linear Equations in 2 Variables S.Y.Tan

Solve the following systems of linear equations: Consistent independent system: One solution Graphically: intersecting lines S.Y.Tan

one point of intersection S.Y.Tan

Inconsistent system : NO solution Graphically: parallel lines S.Y.Tan

Consistent dependent system: Infinitely many solutions Graphically: coincident lines S.Y.Tan

Consistent independent system: one solution S.Y.Tan

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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. S.Y.Tan

Solve the following systems of 3 Linear Equations in 3 Variables: S.Y.Tan

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Solve the following systems of 3 Linear Equations in 3 Variables: S.Y.Tan

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Solve the following systems of 3 Linear Equations in 3 Variables: S.Y.Tan

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System of Linear and Non-linear Equations in 2 Variables Solve the following systems of non-linear equations: S.Y.Tan

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. S.Y.Tan

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quadratic equation in one variable linear quadratic quadratic equation in one variable S.Y.Tan

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