System Equations

This week in math 10 we focused on systems of linear equations. We were taught 3 different ways of finding the possible solutions. We learned about graphing, substation ann or elimination. Using any of these 3 options will give you the same answers. The one I found easiest was elimination.

When using elimination the biggest thing you want to do is create a zero pair with either the X or Y. Elimination can use either addition or subtraction, I will be using addition in my example because I find it easier and you’re less likely to mix up your positives and negatives.

Step 1: Rearrange equations if necessary. The zero pairs may not always be visible, if that’s the case you may need to multiply either one equation or both, so that either the X or Y makes a zero pair.

Step 2: Once you have your zero pair add both equations together. (I find it easier when you place one equation directly above the other.)

Step 3: Depending on what was you zero pair was your next step will be to isolate the variable that is left.

Step 4: Once you’ve figured out one of your missing variables place that variable in to one of your equations. (I suggestion picking the easier equation.)

Step 5: Once again you will need to isolate the variable. After doing that you should have you missing X and Y variables.

Step 6: It’s always good to verify. Once you’ve found both variables place those variable in your equation, if for both equations are true equations you have done it right. (The variable must work for both equations for it to be correct.)

Example 1: (Zero pair is already given)

-2x + 3y = 4

2x + 5y = 12

Example 2: (Zero pair must be found)

5x – 3y = -1

3x + 2y = 7