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# MTH 108 Quiz: Chapters 10 and 11 Study Guide Notes Premium

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School
Department
Mathematics
Course
MTH 108
Professor
Lun- Yi Tsai
Semester
Fall

Description
MTH 108 Precalculus Mathematics II Chapters 10 and 11 Study Guide Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Substitution ▯ What are steps for solving linear equations by using substitution? – Solve one of the two equations for either of the two variables in terms of the other variable. – Substitute the solved expression into the other equation and solve for the ﬁrst variable. – Substitute the ﬁrst solved variable into either expression and solve for the second vari- able. – Check both solutions to make sure that both are equaled in the original equations. Elimination ▯ What are steps for solving linear equations by using elimination? – Multiply all of the terms of either one or both of the equations by the chosen constants from obtain either of the coeﬃcients for either x or y. – Add both equations to eliminate one of the two variables. – Based on the solved variable, solve for the resulting equation. – Substitute the variable into either of the two equations to solve for the other variable. – Check both solutions to make sure that both are equaled in the original equations. Three Variables Equation The following is the general equation with three variables: Ax + By + Cz = D Instead of (x;y) being its general solution, it’s now (x;y;z), which is also called an “ordered triple”, thanks to the third variable, which is z. xyz-Coordinate System The xy-coordinate system is a 2-dimensional whereas the xyz-coordinate system is a 3-dimensional, which is also thanks to the third variable, which is z. 1 The 3 Planes The following would be the structure on how each of the three planes act as if it was a room corner: Plane Wall xy ▯ plane Floor yz ▯ plane One Wall xz ▯ plane Other Wall Solving Inequalities With Absolute Value Inequalities With Absolute Value Theorem If both a is any positive number and that x is an algebraic expression then the following will occur: jxj < a is equaled to ▯a < x < a jxj ▯ a is equaled to ▯a ▯ x ▯ a In Other Words : jxj < a is equaled to ▯a < x and x > a jxj ▯ a is equaled to ▯a ▯ x and x ▯ a Tip With Solving Inequalities Sign Interval Notation Formation < ( ) ▯ [ ] > ( ) ▯ [ ] Solving Inequalities Using Sign Charts Main Tips ▯ What are the general steps to solve any quadratic inequalities by using a sign chart? – Get zero on one side of the imbalance and after that discover the x-captures of the quadratic capacity on the opposite side. – Plot the given x-values of the various x-intercepts c
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