1. By Stanley Brown & Rodney Lewis

2. It is a extension of the elimination method is to multiply one or both equations in a system by some number so that adding or subtracting eliminates a variable.

3.  Need to know how to do basic elimination Example: 3x-2y=5 -3x+4y=6 http://www.coolmath.com/algebra/12-2x2-systems-of- equations/03-solving-by-elimination-addition-01.htm  Need to know how to solve multi step equations using multiplication and division http://www.coolmath.com/algebra/06-solving- equations/index.html

4. 3x+4y=-25 Multiply by 2 (+) 2x-3y=6 Multiply by -3 6x+8y=-50 -6x+9y=-18 17y = -68 17 17 y=-4  Multiply so that the “X” coefficients are Additive inverses.  Add the equations, The inverses will cancel leaving “Y” by itself  Divide by 17 to find the value of your “Y”  Your “Y” will be -4

5. 2x-3y=6 2X-3(-4)=6 2x+12=6 -12 -12 2x=-6 2 X=-3  To find your X you have to substitute Y back into one of the equations. Y=-4  Multiply -4 by -3  Subtract 12 from both sides of the equations.  Divide each said by 2  X will equal -3  Your final solution will be (-3,-4)

6. 1 st Choose one equation and solve for x or y Solve for y in the 2 nd equation. Multiply by -2-6x-4y=-20 Multiply by 3 (+) 6x-3y=27 2 nd Eliminate Cancels your x value -6x-4y=-20 (+)6x-3y=27 3 rd solve Divide -7y=7Y=-1 7 4 Th Substitute the value found in step 2 back into one of the equations and solve. Your Y value was equal to -16x-3(-1) =27 Subtract 3 from each side6x+3=27 -3 -3 Divide 6 from each side6x=24x=4 6 Your solution will be (4,-1)

7. 1. 2x-y=6 3x+4y=-2 2. 2x+7y=1 x+5y=2 3.4x+7y=6 6x+5y=20 4.x+y=3 2x-3y=16 5. 2x+y=5 3x-2y=4 6.8x-3y=-11 2x-5y=27 7.4x-7y=10 3x+2y=-7 8.12x-3y=-3 6x+y=1 9.1.8x-0.3y=14.4 x-0.6y=2.8 10.3x- ½ y=10 5x+¼y=8

8. Elimination with multiplication  http://www.coolmath.com/algebra/12-2x2-systems- of-equations/03-solving-by-elimination-addition- 02.htm http://www.coolmath.com/algebra/12-2x2-systems- of-equations/03-solving-by-elimination-addition- 02.htm fun way to practice with regular equations  http://www.coolmath-games.com/0- arithmeticgame/index.html Know enough? Try the test  http://www.glencoe.com/sec/math/studytools/cgi- bin/msgQuiz.php4?isbn=0-07-860390- 0&chapter=7&lesson=4&headerFile=6&state=na

9. 1. (5,-1) 2. (4,-1) 3. (5,-2) 4. (5,-2) 5. (2,1) 6. (-4,-7) 7. (-1,-2) 8. (0,1) 9. (10,12) 10. (2,-8)