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.


Graph the system of inequalities.

x - 2y

≤ 0

> 2



Step 1 Solve the first inequality for y. Then graph the inequality.

The first inequality does not contain the variable y.

To graph the first inequality, x 0, first graph the corresponding equation, x = 0.

• This is a vertical line that passes through the x-axis at the point (0, 0); it is the y-axis.

For the inequality x 0, the inequality symbol is “”. This stands for “is less than or equal to.”

• To represent “equal to,” draw a solid line along the y-axis.

• To represent “less than,” shade the region to the left of the line. Each point in that region has an x-coordinate less than 0.

Step 2 Solve the second inequality for y. Then graph the inequality.

To solve x - 2y > 2 for y, do the following:

Subtract x from both sides. - 2y > - x + 2
Divide both sides by -2. Be sure to reverse the inequality symbol because you are dividing by a negative number.
To graph , first graph the equation .

• The y-intercept is (0, -1). Plot (0, -1).

• The slope is . To find a second point on the line, start at (0, -1) and move up 1 and right 2 to the point (2, 0). Plot (2, 0).

• Since the inequality symbol “<” does not contain “equal to,” draw a dotted line through (0, -1) and (2, 0).

• To represent “less than,” shade the region below the line.

Step 3 Shade the region where the two graphs overlap.

The solution is the region where the graphs overlap.

The solution of the system is the dark shaded region.

As a check, choose a point in the solution region.

For example, choose ( -1, -5).

To confirm that ( -1, -5) is a solution of the system, substitute -1 for x and -5 for y in each of the original inequalities and simplify.

First inequality Second inequality


Is -1

≤ 0

≤ 0 ? Yes





x - 2y

-1 - 2(-5)

-1 + 10


> 2

> 2 ?

> 2 ?

> 2 ? Yes


Since ( 1, 5) satisfies each inequality, it is a solution of the system.