Non Linear Equations Study Guide
System of Non-Linear Equations Start this lesson by answering the warm-up questions below. This is to assess the ideas or concepts related to Non-linear and Linear equations. Activity 1.5.a Linear Against Non-Linear Equations Answer the following questions below: 1. Determine if the equation is linear or not a. 2x + 3y – 4 = 0 b. xy + 2 = 0 c. x = y d. y = 0 e. x = 2y + 3 2. Which of the following is a non-linear equation? a. 2x2 + 3y – 4 = 0 b. xy + 2 = 0 c. x2 – y = 2 d. 2x + 3y – 6 = 0 e. x = y System of Non-Linear Equations I. Definition of System of Non-Linear Equations Non-linear equations involve two or more equations of the second degree in the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Non-linear curves are circle, parabola, ellipse, and hyperbola. Possible non-linear equations involve the combinations of the equations of the circle, parabola, ellipse, and hyperbola. …show more content…
The solution of the system is the intersection point of the graphs of the given equations. II. Solution of the System A system of equations can be solved through Eliminations method, Substitution method or by a Graphical method. A. By elimination method Example 1: Solve the system of equation by elimination method x2 + y2 = 4 - eq’n (1) x2 - y2 = 4 - eq’n (2) Assigning equation (1) & (2) and eliminate y variable by adding the two equations, we have 2x2 = 8, and solving for x x2 = 4 → x = ±2 Using the value of x and solving for y using eq’n (1) (±2)2 + y2 = 4 4 + y2 = 4 y2 = 4 - 4 y2 = 0 → y =
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