Solving Systems of Equations 3 Approaches Click here to begin Mrs. N. Newman

Method #1 Graphically Door #1 Method #2 Algebraically Using Addition and/or Subtraction Door #2 Method #3 Algebraically Using Substitution Door #3

In order to solve a system of equations graphically you typically begin by making sure both equations are in standard form. Where m is the slope and b is the y-intercept. Examples: y = 3x- 4 y = -2x +6 Slope is 3 and y-intercept is - 4. Slope is -2 and y-intercept is 6.

Graph the line by locating the appropriate intercept, this your first coordinate. Then move to your next coordinate using your slope.

Use this same process and graph the second line.

Once both lines have been graphed locate the point of intersection for the lines. This point is your solution set. In this example the solution set is [2,2].

In order to solve a system of equations algebraically using addition first you must be sure that both equation are in the same chronological order. Example: Could be

Now select which of the two variables you want to eliminate. For the example below I decided to remove x. The reason I chose to eliminate x is because they are the additive inverse of each other. That means they will cancel when added together.

Now add the two equations together. Your total is: therefore

I decided to substitute 3 in for y in the second equation. Now substitute the known value into either one of the original equations. I decided to substitute 3 in for y in the second equation. Now state your solution set always remembering to do so in alphabetical order. [-1,3]

Lets suppose for a moment that the equations are in the same sequential order. However, you notice that neither coefficients are additive inverses of the other. Identify the least common multiple of the coefficient you chose to eliminate. So, the LCM of 2 and 3 in this example would be 6.

Multiply one or both equations by their respective multiples Multiply one or both equations by their respective multiples. Be sure to choose numbers that will result in additive inverses. becomes

Now add the two equations together. becomes Therefore

Now substitute the known value into either one of the original equations.

Now state your solution set always remembering to do so in alphabetical order. [-3,3]

In this example it has been done for you in the first equation. In order to solve a system equations algebraically using substitution you must have on variable isolated in one of the equations. In other words you will need to solve for y in terms of x or solve for x in terms of y. In this example it has been done for you in the first equation.

Choosing to isolate y in the first equation the result is : Now lets suppose for a moment that you are given a set of equations like this.. Choosing to isolate y in the first equation the result is :

Now substitute what y equals into the second equation. becomes Better know as Therefore