Question 108989
Hello.

Eq (1)    10x + 2y = 7
Eq (2)                  y = -5x + 3


Notice that if we add 5x to both sides of equation (2) we will get:

               5x + y = 3


Now forming our modified system of equations we get:


                 10x + 2y = 7
                   5x +   y  = 3

Now here is the important part. To solve by addition or subtraction we will need to multiply Eq (2) by a some number that will let us clear out the "x" variable. 

Here is what to do:

              Step 1.     Multiply Eq (2)  that is      2 * (5x + y = 3 )   which should give us  10x + 2y = 6. 
              Step 2.    Now we can subtract Eq (2) from (1).    
 
                                            10x + 2y  = 7
                                    -      10x + 2y  = 6
                                           _______________
                                              0x  + 0y = 1             

(which is inconsistent since zero of something clearly can not equal one of something.)

Another way to look at the problem is with substitution. 

For example in the original system:

                     10x + 2y =  7
                                   y =  -5x +3

          The second equation is already solved for the variable "y." We could just simply substitute that equation for the instance of Y in the first equation

                     10x + 2(-5x+3) = 7   

          Which expands to:

                     10x -10x + 6 = 7

          And that simplifies to:

                         6  =  7      (which is clearly not true) So we can see that the system in inconsistent. 


Finally, a unique solution to this system is impossible.