Different Ways to Graph Equations

I  Finding x and y intercepts

   Keep the equation in standard form ax + by = c

   Find the points where the equation crosses the x and y intercepts by substituting with zero

   3x + 5y = 30                            3x + 5y = 30

   3(0) + 5y = 30                         3x + 5(0) = 30

               y = 6                                x = 10

 y intercept (0, 6)                   x intercept (10, 0)

Plot the y intercept THEN  the x intercept and put a line through the two of them

II Rewrite in slope intercept form y = mx + b

     3x + 5y = 30

     5y = -3x + 30    then divide everything by 5

      y = - 3/5x + 6

     Plot the y intercept which is 6 THEN plot the slope by going down 3 to the right 5

http://www.purplemath.com/modules/systlin2.htm for a review of no solution vs many solutions

http://www.kutasoftware.com/FreeWorksheets/Graphing%20Lines%20SI.pdf for practice graphing in slope intercept form with answers at the end

http://www.kutasoftware.com/FreeWorksheets/Systems%20of%20Equations%20Graphing.pdf graphing systems in slope intercept form with answers

Solving Systems of Equations: Substitution

Rewrite one of the equations either into y =         OR x =

        2x - 3y = -9 and   x + 4y = 1

       rewrite x =  - 4x + 1 since it is easier than rewriting the other equation; look for the variable that has the invisible one

Then substitute the one you rewrote into the other equation and solve

    2(-4x + 1) - 3y = -9 x + 4y = 1

   -8y + 2 - 3y = -9

    -11y + 2 = -9  by combining like terms

    - 11y = -11

         y = 1

Now take your answer and substitute it into the other equation to solve for the opposite variable

     x + 4(1) = 1

           x = -3x + 4y = 1

Check your solution  (-3, 1) by substituting them into the original two equations   and 2x - 3y = -9

    1(-3) + 4(1) = 1  True

    2(-3) - 3(1) = -9 True

http://www.purplemath.com/modules/systlin4.htm  for detailed examples

Systems%20of%20Equations%20Substitution.pdf for extra problems to practice with answers at the end 

Solving Systems of Equations: Elimination by Addition or Subtraction

http://www.purplemath.com/modules/systlin5.htm

Solving Systems of Inequalities:

1st rewrite the equation in slope-intercept form y=mx+b; the y MUST BE POSITIVE!

***Remember as you are rewriting it, if you have to divide by a negative y then you need to switch the inequality symbol

2nd graph the equation (like we did back in chapter 3) as if it were an equation

3rd now graph it as an inequality by looking at if y is greater/equal or less than/equal and use a dashed or solid line

4th use a test point to see if you shaded in the right direction

Now repeat the process for the other equation

http://www.purplemath.com/modules/syslneq.htm  detailed explanation

http://regentsprep.org/regents/math/math-topic.cfm?TopicCode=sysineq more help

http://regentsprep.org/regents/math/sysineq/PracGr.htm practice