Find the choice below which gives a first step in solving 
the given system of equations by the addition method. 
2x - 3y = 7 
 x - 4y = 2 
(Points: 10)
Multiply the first equation by 3 and the second by 4. 
Multiply the first equation by -4 and the second by -2. 
Multiply the second equation by -2. 
Multiply the first equation by 4.

Let's try the first choice:

Multiply the first equation by 3 and the second by 4.

2x - 3y = 7  becomes 6x -  9y = 21
 x - 4y = 2  becomes 4x - 16y = 8

Will the terms in x or y cancel if I add the two 
new equations and get a third new equation in only 
one letter? 

No because when I add those two new equations:

 6x -  9y = 21
 4x - 16y =  8
--------------
10x - 25y = 29

Nothing canceled out and the resulting equation still contains two 
variables, x and y, so the first choice is not correct.   

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

Now let's try the second choice:

Multiply the first equation by -4 and the second by -2.

2x - 3y = 7  becomes -8x + 12y = -28
 x - 4y = 2  becomes -2x +  8y =  -4

Will the terms in x or y cancel if I add the two 
new equations and get a third new equation in only 
one letter? 


No because when I add those two new equations:

 -8x + 12y = -28
 -2x -  8y =  -4
----------------
-10x +  4y = -32

Nothing canceled out and the resulting equation still contains
two variables, x and y, so the second choice is not correct 
either. 

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

Let's try the fourth choice:

Multiply the first equation by 4. Note: Nothing was said in this
choice about multiplying the second at all, so that is to be 
interpreted as leaving the second equation just as it is, or
multiplying it by 1.  

2x - 3y = 7  becomes   8x - 12y = 28
 x - 4y = 2  stays as   x -  4y =  2

Will the terms in x or y cancel if I add the two 
new equations and get a third new equation in only 
one letter? 

No because when I add those new first equation to the old
second equation:

  8x - 12y = 28
   x -  4y =  2
----------------
  9x - 16y = 30

nothing canceled out and the resulting equation still contains 
two variables, x and y, so the fourth choice is not correct either. 

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

Let's try the third choice:

Multiply the second equation by -2. 

Note: Nothing was said in this choice about multiplying the first
at all, so that is to be interpreted as leaving the first equation
just as it is, or you could say, multiplying it by 1.  

2x - 3y = 7  stays as  2x - 3y =  7
 x - 4y = 2  becomes  -2x + 8y = -4

Will the terms in x cancel if I add the old first equation
to the new second equation and get a third new equation in 
only one letter? 

YES INDEED! Because when I add the old first equation to the new
second equation:

  2x - 3y =  7
 -2x + 8y = -4
----------------
     - 5y =  3

The 2x and the -2x canceled out and the result is an equation
in just ONE variable y, so the third choice is INDEED the correct
choice.

Edwin