SOLUTION: linear systems by addition i cannot figure this one out 3x-7y=13 6x+5y=7

In solving systems of linear equation, we can do it by sustitution method
Elimination or graphing.

You are told to solve it by addition or Elimination Method.
We are to eliminate one variable then solve for the other variable.

say we have 3x - 7y = 13 
      and   6x + 5y = 7

Now, you choose which variable to eliminate.Choose x
Since we have 3x and 6x by adding them we cant eliminate that variable.
So we need to multiply a certain number to do that.
          
             -2(3x - 7y = 13)  multiply -2 to the first equation
               (6x + 5y = 7)

             -6x + 14y = -26  Notice that if -6x + 6x = 0
              6x +  5y =  7   x is eliminated y is left.
              _____________
                 + 19y = -19  Then solve for the other variable y.
                    
                   19y = -19  Divide both sides by -19
                     y = -1

Then substitute the value of y which is -1 to any of the 2 equations

     3x - 7y = 13, y = -1

     3x - 7(-1) = 13
         3x + 7 = 13
     3x + 7 - 7 = 13 - 7       subtract 7 both sides
             3x = 6            Divide both sides by 3
              x = 2

So the solution is (2, -1)

If you want to check if your answer is right,
Substitute x = 2 and y = -1 to both equation.
If both equation were true after substituting, then your answer is correct.
You try checking ok.

Happy calculating

Rachel