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**Unformatted text preview: **MATH 006 Calculus and Linear Algebra (Lecture 5) Albert Ku HKUST Mathematics Department Albert Ku (HKUST) MATH 006 1 / 16 Outline 1 Systems of Linear Equations in Two Variables 2 Types of Linear Systems Albert Ku (HKUST) MATH 006 2 / 16 Systems of Linear Equations in Two Variables Systems of Linear Equations in Two Variables The following is an example of systems of linear equations in two variables . Example Given the following system of linear equations: x- 2 y = 2 x + y = 5 Find its solution. Remark A collection of equations is called a system . There are two unknowns (or variables) x and y in the system. To find a solution to the system, we need to find the values of x and y that satsify the two equations in the system. Albert Ku (HKUST) MATH 006 3 / 16 Systems of Linear Equations in Two Variables Algebraic and Graphical Methods We solve it by two algebraic methods: 1 Method of substitution 2 Method of elimination We can also solve it by graphical method . Albert Ku (HKUST) MATH 006 4 / 16 Systems of Linear Equations in Two Variables Method of Substitution For the system x- 2 y = 2 (1) x + y = 5 (2) Rewrite (1) as x = 2 + 2 y (3) and substitute it into (2): (2 + 2 y ) + y = 5 Solving, we get y = 1....

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