Elimination Steps

Nota:

• * Answer = were two lines on a graph intercept.

1. 1. Check if both equations have the same variables and numbers.

   Nota:

   • 14x = 5y = 11                                               7x + 3y = 16 * In this equation, they don't. 
2. 2. If not, multiply or divide the two (or one) variable(s) so they cancel each other out.

   Nota:

   • 14x + 5y = 11                                                                     7x + 3y = 16 * You could divide 14 by 2( 7 and 7), multiply 7 by 2 ( 14 and 14), or multiply 5 by 3 (15 and 15).
3. 3. Subtract or add so that the variable and number equal zero.

   Nota:

   • * You subtract when both numbers are negative or both are positive. ex: -3 - -3 = 0   ex: 4 - 4 = 0
   • * You add when one number is negative, and the other is positive, or the other way around. ex: -5 + 5 = 0  ex: 9 + -9 = 0
4. 4. Solve this new equation.

   Nota:

   • 14x + 5y = 11 becomes 42x + 15y = 33 7x + 3y = 16 becomes 35x + 15y = 80 
   • 1. 42x - 35x = 7x 2. 15y - 15y = 0 3. 33- 80 = -47
   • New equation = 7x = -47 Answer ~ x = -6.71
5. 5. Plug answer into one of the equations. Then, solve.

   Nota:

   • 35( -6.71) + 15y = 80  Answer ~ y = -9.06
6. 6. Answer can be written like this: (x, y). Or this: x=_ y=_

   Nota:

   • x = -6.71  y= -9.06