Algebra Tutorials!
 
 
   
Home
Rational Expressions
Graphs of Rational Functions
Solve Two-Step Equations
Multiply, Dividing; Exponents; Square Roots; and Solving Equations
LinearEquations
Solving a Quadratic Equation
Systems of Linear Equations Introduction
Equations and Inequalities
Solving 2nd Degree Equations
Review Solving Quadratic Equations
System of Equations
Solving Equations & Inequalities
Linear Equations Functions Zeros, and Applications
Rational Expressions and Functions
Linear equations in two variables
Lesson Plan for Comparing and Ordering Rational Numbers
LinearEquations
Solving Equations
Radicals and Rational Exponents
Solving Linear Equations
Systems of Linear Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS
Solving Quadratic Equations
Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
Systems of Linear Equations
Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
SOLVING LINEAR AND QUADRATIC EQUATIONS
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
   
Try the Free Math Solver or Scroll down to Resources!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

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


Linear equations in two variables

Key Concepts: Ordered pairs/The Rectangular Coordinate system
Solutions to equations with 2 variables
Linear equations in two variables
Intercepts
Horizontal and Vertical lines


Martin-Gaye sections and practice problems

3.1: 1 – 19 odd, 23 – 51 odd, 55, 57
3.2: 1 – 43 odd, 47, 53, 55
3.3: 1 – 10 all, 11 – 63 odd

Definitions
A solution to an equation with two variables, x and y , is an ordered pair (a,b) where a and b are
real numbers with the property that if x = a and y = b the equation is true. The number a is called
the x-coordinate of the ordered pair and the number b is called the y-coordinate of the ordered pair.

Example 1
What are the x and y coordinates of the ordered pair (9,− 2) . Is the ordered pair a solution to
the equation 3 x + 4 y = 10 + x ?


Example 2
What is the ordered pair with a x-coordinate of 5 that satisfies the equation y = 6 x + 4


Example 3
What is the ordered pair with a y-coordinate of 5 that satisfies the equation y = 6 x + 4


Example 4
Write the missing values into Table 1 so that each implied ordered pair is a solution to the equation
x + y = 4. Plot the four ordered pairs onto Figure 1.

Table 1: x + y = 4

Example 5
The sum of the the coordinates of each point on the line in Figure 2 is always the same number.
What is this constant sum?

Example 6
Several points are shown in Figure 3. State the ordered pair associated with each point and where
in the coordinate plane the point lies; assume that both coordinates of each point are intergers.
Which point, B or F, is a solution to the equation 3x − 2 y = 8 ?

Example 7
Plot the points A(−3, 4) , B(−3, −3) , and C(5, 2) onto
Figure 4 and find the area, A, of the resultant triangle.
Assume that the scale on each axis is in centimeters.

Example 8
At each point on the line in Figure 5, twice the x-coordinate minus the y-coordinate is always the
same number. What is this common difference?

  Copyrights © 2005-2017