1. 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

2. 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

3. 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

4. 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

5. 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

6. 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)]

7. 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

8. 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

9. 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

10. 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

11. 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