When solving by the addition​ method, we can eliminate x by multiplying the first equation by​ ________ and then adding the equations.?

Question

When solving by the addition method, we can eliminate x by multiplying the first equation by ________ and then adding the equations.?

Answer 1

Hi Ken from Little Rock, AR...hope you're having a good weekend.

Thanks for connecting with Wyzant...I am here to help.

 

When solving by the addition method, we can eliminate x by multiplying the first equation by ________ and then adding the equations.?

 

With this statement, you are going to prove what the first step is required to using the Addition Method in solving a linear equation.

Example:      2x + y = 6    and the equation    x - 2y  = -17    What these two equations together mean, is that then you put the values we solve for x and y, it would be true for each equation. So what steps do you take, Using the Addition Method, to solve this problem? Here is what you do:

Your goal is to some how remove the x value, BUT not change value of the entire equation. When your teacher asks to remove a value using the Addition Method, it sounds confusing RIGHT? Adding something means you put something to it, so how does that remove it? The only way to remove something is to take it away, or SUBTRACT...but is says to ADD! So...let's add a negative value, which is the same as subtraction.

 

You have the two equations:     2x + y = 6         x - 2y = -17      and your goal is to remove the x values: one x value is 2x and the other is just x

What you will do is rewrite each of the equations over each other:

 

              2x  +  y  =    6 

                x  - 2y  =  -17          Multiply the entire equation by -2

                                               change its look but not its value

 

             2x   +   y   =    6

          -2[x    -  2y   = -17]        Complete the operation

 

            2x   +     y   =   6

           -2x   -  -14y  =  24    Make sure you check the signs, then rewrite

 

            2x   +    y   =   6

           -2x  + 14y   =  24       Now you ADD the 2 equations together..

             0        15y  = 30       You see how you have removed the x value

 

              15y  =  30                Continue solve for y, divide both sides by y

               15       15                Which leave us with

 

                  y  =  2                 After you solve for y, then you put the 

                                             y value into your equations and solve for x

  

So let's complete your sentence:

When solving by the addition method, we can eliminate x by multiplying the first equation by the negative inverse of the x value so that when you add them together, you get zero and then adding the equations.?

 

 

I hope this helps, if you need any further help, contact me on Wyzant