how to solve both problems by elimination step by step

Question

7x+3y=-12

-7x+2y=-8

 

2x+8y=8

3x-2y=-16

Answer 1

Hello, Britt

 

Well the first problem is almost done.  Add the top to the bottom equation

 

#1

 

7x+3y= -12

-7x+2y=-8                           -7x+ 7x cancelled each other out.  3y+2y=5y

      5y=-20                          Divide both sides by 5

        y=- 4                          

 

To find the value of x, you must plug in -4 for y into either equation.  I am going to choose 7x+3y=-12.

 

7x+3y= 12                          Plugging 4 for y

7x+3(-4)=-12                      Multiplying on the left side

7x-12=-12                           Add 12 to both sides

    +12   +12

     7x=0                            Divide by 7 on both sides

      x=0

S0, the answer is (0,-4).  Next, check you answers.  7(0)+3(-4)=-12... -12=-12.  So, it appears to be the correct answer.  But try both of them.  -7(0)+2(-4)=- 8...   -8=-8  . True.  So , (0,-4) is the correct answer for this system of linear equations.

 

#2  is a little more complicated.  You can do this problem in literally millions of ways, but the simplest way will be to multiply the bottom equation by 4.  Why is this the easiest?  Because by performing one operation, you can eliminate one variable right away, y.  Yes, you can eliminate y, in many different ways, but that will require many more calculations.  And the more calculations you perform in math, the more chances that you will make a mistake.  So, lets gets stated by multiplying the bottom equation by 2. And the finding the value of x.  Finally, substituting the value of into either of the original equations. 

 

2x+8y= 8

3x-2y= -16           

 

Multiplying this equation by 8.  I want to make -2y into -8y.

   2x   +8y= 8

4(3x   -2y= -16)

 

   2x+8y= 8

  12x-8y= -64   Used the distributive property

   14x= -56     -8y and 8y cancelled each other out.

     x= -4    Divided both sides by 14

 

Plugging -4 for x into the first equation.  2(-4)+8y= 8

                                                           -8  +8y  =8

                                                             +8        +8                                   

                                                                  8y= 16

                                                                   y=2

  

(-4, 2)  should be our answer.  Of course, don't forget to check your answer.

 I hope this helps and please rate my answer :)

 

D. Y. Taylor