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**Solving Algebraic Equations**

4/11/2017 Math Review with Matlab: Solving Algebraic Equations Algebraic Equations with Multiple Variables S. Awad, Ph.D. M. Corless, M.S.E.E. D. Cinpinski E.C.E. Department University of Michigan-Dearborn

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**Solving Algebraic Equations with Multiple Variables**

Solve Command for Equations of Multiple Variables Single Equation of Two Variables Example Two Variable Complex Solution Example System of Equations Example System of Equations with Symbolic Constant Example

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**Solve Command for Equations of Multiple Variables**

The solve command can be used to solve symbolic expressions with more than one variable: solve(f) solves the symbolic expression f using the symbolic variable closest to x as the independent variable solve(f, v) solves the symbolic expression f in terms of the independent variable v

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**Single Equation of Two Variables Example**

Given the equation: 1) Find the solution of the equation assuming that c is the solution variable 2) Find the solution of the equation assuming that b is the solution variable

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**Default Solution Solve for c as the independent variable**

c is the default variable since it is closest to x » syms b c » f=b^2+4*c+2*b; » sol_c=solve(f) sol_c = -1/4*b^2-1/2*b

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**Solve for b Solve for b as the independent variable**

b must be explicitly specified on the command line » sol_b=solve(f,b) sol_b = [ -1+(1-4*c)^(1/2)] [ -1-(1-4*c)^(1/2)]

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**Two Variable Complex Solution Example**

Given the equation of two variables: Solve for x in terms of y using Matlab: » syms x y » xs=solve(x^2+9*y^4) xs = [ 3*i*y^2] [ -3*i*y^2] Roots are Complex Conjugates

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**System of Equations Example**

Solve the system of consistent linear equations: » syms x1 x2 x3 » f1='3*x1-x2+2*x3=12'; » f2='x1+2*x2+3*x3=11'; » f3='2*x1-2*x2+x3=2'; » [x1 x2 x3]=solve(f1,f2,f3) x1 = 7 x2 = 5 x3 = -2

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**System of Equations with Symbolic Constant Example**

Solve the two equations: x and y are independent variables a is a constant » syms x y a » s=solve(x+6*y-a,2*x-3*y-9) s = x: [1x1 sym] y: [1x1 sym] s is a structure

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Viewing Structures The solution is a structure with named fields x and y representing symbolic expressions s = x: [1x1 sym] y: [1x1 sym] » xs=s.x xs = 18/5+1/5*a » ys=s.y ys = -3/5+2/15*a View each symbolic expression separately Expressions are in terms of symbolic variable a

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**Summary The solve command can be used to solve:**

A single equation in terms of an independent variable A system of multiple consistent equations A system of equations having symbolic variables and symbolic constants

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