Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.

 It is important to note that some equations have decimals or fractions as coefficients. Systems do not always have nice integers in the solutions

Example 1:

When the equations have fraction coefficients we must multiply each equation by its LCM to obtain integral coefficients.

  and  find 

Now we must multiply each equation so that one of the variables has coefficients that are “equal and opposite”.

  now find

Add the equations then simplify to get x = 56

Replace x = 56 in the equation: 7(56) − 6y = 2

392 − 6y = 2 Add opps: - 6y = - 390

multiply recip: to find y = 65

Check the values in both equations The solution point: { (56, 65) }


Addition Method:

Add two equations in a system of equations, and obtain another equation in the system (having the same solution). Also multiply an equation by a real number and obtain another equation in the system, and combine the two processes.

The object in the Addition Method is to add two of the equations in order to eliminate one of the variables. The resulting equation can then be solved for either x = h or y = k and which can then be used as a replacement in one of the given equations to find the value of the other one.


Example 2:

Multiply the first equation by -4

Now add and get

This gives

Replace in the first equation:

Check the values in both equations

The solution point:


Example 3:

(1) See that the LCM of the 1st equation is 12 and of the 2nd is 6.

(2) Multiply each by the LCM’s

(3) Now solve the simplified system --.

  To get equal and opposites multiply the 1st by 2 and the 2nd by +3 then add the results:

Replace x = 2 in (3): 4(2) + 3y = 14 which yields y = 2

Check: Always check your answers.

Go back to the original equations and substitute both: 

They checked -- now write the solution as S = { (2, 2) }