Your Algebra Homework Can Now Be Easier Than Ever!

Solve Linear Systems by Graphing

Goal : Solve a system of linear equations graphically

Your Notes

VOCABULARY
Systems of linear equations Two or more linear
equations in the same variables
Solution of a system of linear equations An ordered
pair that satisfies each equation in a system of
linear equations in two variables
Consistent independent system A linear system that
has exactly one solution

Example 1 Check the intersection point

Use the graph to solve the system. Then check your solution algebraically.

Equation 1
Equation 2


Solution
The lines appear to intersect at the point (2,-1).
 

Check Substitute 2 for x and -1 for y in each equation.

Because the ordered pair (2,-1) is a solution of each
equation, it is a solution of the linear system.

SOLVING A LINEAR SYSTEM USING THE GRAPHAND- CHECK METHOD

Step 1
Graph
both equations in the same coordinate
plane. For ease of graphing, you may want to
write each equation in slope - intercept form .

Step 2
Estimate the coordinates of the point of
intersection .

Step 3
Check the coordinates algebraically by
substituting
into each equation of the original
linear system.

Example 2 Use the graph-and-check method

Solve the linear system:

Equation 1
Equation 2

Solution

Step 1
Graph
both equations.

Step 2
Estimate the point of intersection. The two lines
appear to intersect at ( 2 , 3 ).

Step 3
Check whether ( 2 , 3 ) is a solution by
substituting 2 for x and 3 for y in each of
the original equations.

Equation 1 Equation 2

Because ( 2 , 3 ) is a solution of each equation in the
linear system, it is a solution of the linear system.

Guided Practice Solve the linear system by graphing.

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of December 12th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2017, Algebra-Answer.Com.  All rights reserved.