Math
Please read the information in the above prompt and note the topics covered in week 4 as well as instructions given relating to your Initial Post. I have videos on each of the week 4 topics in the announcements for additional help.
I am getting us started by giving you an example solved using both the Substitution and Elimination methods.
I hope you find it helpful.
EXAMPLE PROBLEM
I thought I would show you an example solving the following system of equations using first the Substitution Method and then the Elimination Method:
2x+y=8 x-y=1
First, I will use the Substitution Method. Solving for x in the second equation yields x=1+y. Now, substitute this into the first equation in place of x. 2(1+y) + y=8 We must now simplify this equation. 2+2y+y=8 After combining like terms on the left we have 2+3y=8 Now solve for y by subtracting 2 on both sides. 3y=6 Now divide both sides by 3, which gives y=2. This can be substituted into either equation to solve for x. In the second equation, x-2=1 Now add 2 to both sides which gives x=3. The solution to the system is x=3, y=2 which gives the point represented by the ordered pair (3,2).
Next, I will solve this system of equations by the Elimination Method which is sometimes called the Addition Method. This method calls for us to line up like terms beneath one another, which is already done in our example. We want to be able to add the two equations and eliminate one of the variables. Our example is set up to eliminate y. If this was not the case, you would need to multiply one of the equations by the necessary constant to make this happen. 2x+y=8 x -y=1 ——— 3x = 9 This is found by adding the two equations. Now divide both sides by 3, to get x=3. Substitute 3 in place of x in either equation to solve for y. I will use the first equation. 2(3) + y=8 now 6+y=8 next we subtract 6 on both sides which gives y=2. The solution is (3,2)
You will get practice with both of these methods this week as well as solving a system using the Graphing Method. Let us know which of the 3 methods you like best and why.
Now let’s get started:
**Post a problem and show your step-by-step solution using one of the three methods. Dont forget to do a check. Put your solution into your original problem. Does it work?
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