2. By Carol Nicholson

3.  When we have two lines on the same plane:

5.  Easiest question of the day!  Put both equations into slope intercept form. Y = mX + b  If the slope is the same – look at the Y-intercept.  If the slopes are equal but with different Y-intercepts – the lines are parallel.  If the slopes are equal AND have the same Y-intercept – the lines are in fact – the same line.

6.  1) Graphing  2) Substitution Method  3) Addition Method

7. The answer is (-1, -2)

8. 2Y = 4X + 6 Y – X = 8 1 st equation becomes: 2Y = 4X + 6 2 2 2 Y = 2X + 3

9. Y = 2X + 3 Y – X = 8 Next step: Y – X = 8 (2X + 3) – X = 8 Now solve for X Your solution is: X = 5

10.  Now that you know x = 5 2Y = 4X + 6 becomes 2Y = 4(5) + 6 or Y – X = 8 becomes Y – (5) = 8 Either way you get Y = 13 Your solution is (5,13)

11. So what does (5,13) mean? It is the solution, or the point where the two lines meet.

12.  This is exactly as it sounds.  You will add the two equations together.  This is used when you can easily eliminate one variable. An example is : 2y + 3x = 16 2y + 2X = 12 This will work easily because there are same values for y

13. 2y + 3x = 16 2y + 2X = 12  Since both values of y are equal you can multiply either the top equation or the bottom equation by -1. 2y + 3x = 16 - 2y - 2x = -12 x = 4

14. To Review: you can solve by:  Graphing  Substitution Method  Addition Method Original music by James Nicholson