Solve by addition

Question

(a)2x=3y+11

     7x-4y=6

 

(b) 2x=2-y

     3x+y=-1

Answer 1

Solving one of these. The 'addition' method requires first putting both x & y terms on one side of each equation:

2x - 3y = 11

7x - 4y = 6

 

Now STUDY these equations to see what multipliers can be chosen so that the new equations, when summed, will eliminate one of the variables.  I will choose 7 as the multiplier for the first equation, and NEGATIVE 2 as the multiplier for the second of this pair of equations.  Thus:

 

14x - 21y = 77

-14x +8y = -12

________________

       -13y = 65

            y = -5.  Finally, then, put this y back into the original first equation to determine x.

 

Study this until the idea gets across--i.e. understand why the choices of multiplier were made, to eliminate x!

 

Always remember to check your answers, also.