Solve by using the addition method

Question

0.4x - 0.6y = 0.5
0.2x – 0.3y = 0.7

Answer 1

See:   https://www.wyzant.com/resources/answers/169997/solve_by_using_the_addition_method

Answer 2

Solve by using the addition method
0.4x - 0.6y = 0.5
0.2x – 0.3y = 0.7

 

Some people are really good at decimals, but I'm not.  So, I'll multiply both equations by 10 to get rid of the decimal points.  PLZ notice that this produces exactly the same lines as before (they just look simpler).

 

4x - 6y = 5

2x - 3y = 7

 

Now, the Elimination Method either adds or subtracts two equations to eliminate one of the variables.  In order to do this, the coefficients must be opposites (for addition) or the same (for subtraction).  Since the problem statement said to use the addition method, let's multiply the second equation by (-2) [note: this will produce the same result as the subtraction method].

 

   4x  - 6y =   5

  -4x + 6y = 14

-----------------------

    0  + 0   = 19             [Now, wait a minute!]

 

We could have multiplied the second equation by (+2) and seen that they are the same on the left side:

    4x - 6y = 5

    4x - 6y = 14

 

Now, you have a choice:

  (1) put the equations into slope-intercept form and find that the have the same slope (2/3)

  (2) realize that the slope is (-A/B) when the equation is in Standard Form  (slope=4/6=2/3)

 

Lines that have the same slope are parallel.  That means there is no point of intersection (no "solution" to this system).