Solve the system of equations by the addition method. If a system contains decimals, you may want to first clear the equation of decimals.

Question

Solve the system of equations by the addition method. If a system contains decimals, you may want to first clear the equation of decimals.

 

0.02x+0.02y=-0.12

-0.1x+0.3y=-0.4

Answer 1

If the first equation has all of its terms multiplied by 100, then the coefficients become integers; you might also want to then divide all of those coefficients by two.

 

The second equation cleans up nicely if you multiply all terms by ten.

 

Then the final work involves no decimals, and that's a relief. The rest of the work is easier now.

Answer 2

Hi Mailan...of West Palm Beach, FL...hope you had a great day at school.

Great question...I am going to get you started with answering these questions...as a teacher I am not going to give you the answer. I'll help you get started. Make sure you understand and practice these so you will understand the concept of solving for the unknowns.

Here goes...I'll begin and you will need to complete the rest:

         1st Equation:          0.02x +  0.02y  =  -0.12

        2nd Equation:         -0.1x   +  0.3y   =   -0.4

With the addition method, your goal is to add one equation to another so that either variable[make sure you know what variable means]equals zero

                         x  =  0       or     y   =  0

Looking at both equations if we add the x values together it would not equal zero. That goes the same for adding the y values. You will notice that the x values, on of the is a negative value,       −0.1x

If we could change the −0.1x  to something and add it to 0.02 we could get:  0x   Right?    ?x  +  0.02x = 0    How about   −0.02x  + 0.02x = 0x

So how do you change -0.1x   to    −0.02x

How we do that is multiply    -0.1x times 0.2   or (-0.1x)(0.2) =  −0.02x

Got that? Make sure you do, because this is how these problems are answer. Now, we can just multiply the (−0.1x) by (0.2) WE HAVE TO MULTIPLY THE ENTIRE EQUATION BY (0.2). This will change the appearance of the equation but not change the value of the equation.

This is what it will look like:

We will leave the 1st Equation alone:    0.02x   +   0.02y    =    -0.12
Then we multiply the 2nd Equation by 0.2 : 0.2[(-0.1x + 0.3y) = (-0.4)]

               0.02x    +      0.02y    =    -0.12

         (0.2)(-0.1x) + (0.2)(0.3y) = (0.2)(-0.4)   Complete the calculations

 

               0.02x    +     0.02y    =     -0.12

        +   -0.02x     +    0.06y    =     -0.024        now add the equations

                   0x      +    0.06y    =         ?

 

             so       0.06y  =   ?

 

Now you can complete the rest...find the what y equals.

Once you find y  you can calculate for x

You will need to know how to set up these equations and solve them. Remember this is the Addition method.