1. Algebra Vol 2 Lesson 6-3 Elimination by Addition or Subtraction

2.  We can solve a system of equations by drawing the graphs and looking for the intersection.  We can also solve a system by solving one equation for one of the variables and substituting it into the other equation.  In this section, we will add or subtract the equations together to get a new equation that only has one variable.  Similar to the substitution method. Background

3.  The elimination method is useful when the coefficients on one of the variables are either equal or opposites of each other. Indicators Ex 1: 4x+2y=54 2x - 2y=-6 Ex 2: -3x+2y=54 -3x-8y=81 The y-coefficients are opposites The x-coefficients are equal

4.  If we see a system of equations with equal or opposite coefficients, we will add or subtract the equations to eliminate that variable.  Let’s use this idea to solve this system 4x + 2y = 54 2x - 2y = -6 Elimination Method - addition 6x + 0y=48 Now we have one equation with only one variable 6x= 48 x= 8What’s the y-coordinate? The y-coordinates are opposites. Adding the equations will eliminate y.

5.  Continued … 4x + 2y = 54 2x - 2y = -6 Elimination, cont’d So far we know the x-coordinate of the solution is 8. We can use either equation to find the y-coordinate. I’ll choose the first equation. 4(8) + 2y = 54 2y = 22 Now we know the coordinate of the solution is (8,11) 32 + 2y = 54 y = 11

6.  When the system has a pair of equal coefficients, we’ll subtract to eliminate it. 4x + 3y = 24 4x + y = -8 Elimination method - subtraction 0x+2y = 32 y= 16 - ( ) Subtract the second equation from the first. Now plug y=16 back into either equation to find x. 4x+3(16) = 24 4x+48 = 24 4x = -24 x = -6 So the solution is (-6, 16)

7.  Same coefficients » subtract  Opposite coefficients » add  This method will need to be modified to use it on equations that don’t have the same or opposite coefficients.  Only works for a select few systems. Notes