linear equation using the addition method

Question

-3x+6+7y=5

5y=2x 

Solve by using linear equations using the addition method

Answer 1

The addition method of solving systems of linear equations is also known as the method of elimination. 

- 3x + 6 + 7y = 5 ...... (1) 
5y = 2x              ...... (2) 

Let's simplify (1)  

- 3x + 7y = 5 - 6 
- 3x + 7y = - 1   ..... (1.1) 

and move "2x" to the left in (2)

- 2x + 5y = 0  .... (2.1) 

Let's multiply (1.1) by "- 2" and (2.1) by "3" , and add two linear equations 

     6x - 14y = 2 
+ 
  - 6x + 15y = 0      

     0  +  y   = 2  ---> y = 2 

Let's substitute "y" by "2" in (2) 

5 * 2 = 2x 

x = 5

 

The answer is pair of numbers (5, 2) 

Let's check our answer 

- 3 * 5 + 6 + 7 * 2 = 5 
        - 15 + 6 + 14 = 5 
                          5 = 5 

5 * 2 = 2 * 5 
    10 = 10 

Answer 2

Step 1:  Reverse the equation on line 2

-3x+6+7y=5

2x           =5y

Step 2:  Multiply second equation by 3/2 to get the same coefficient for x

-3x+6+7y=5

(3/2)[2x   =5y]

which gives

-3x+6+7y=5

3x           = (15/2)y

Step 3:  Add the two together, noting that the x's cancel out to give one equation in terms of y

6+7y=5+(15/2)y

Step 4:  Move y to right hand side and constants to the left hand side

6-5=(15/2)y-7y

Step 5:  Simplify

1=(15/2)y-(14/2)y

then

1= (1/2)y

2=y

Then substitute back into the equation 5y=2x

5(2)=2x

x=5

 

Double check with first equation:

-3(5)+6+7(2)=5, which is correct.

Answer 3

Rewrite first equation as

 

Eq. 1. 7y - 3x = (5 - 1) = -1

Eq. 2. 5y - 2x =                0

                                        

 

Multiply Eq. 1 by 2 and Eq. 2 by -3

 

Eq. 1a.  14y - 6x = -2

Eq. 2a. -15y + 6x = 0

                                 

 

           -1y           = -2

 

y = 2   

 

7y - 3x = -1

 

7*(2) - 3x = -1

 

-3x = -15

 

x=5