solve by elimination method

Question

8x-y=67

x+7y=44

 

determine solution of the system. select the correct choice below and, if necessary, fill in the answer box to complete your choice

 

a) _ (type an ordered pair)

b) there are infinitely many solutions

c) there is no solution

Answer 1

Elimination means that you want to get to a point where you can add the 2 equations together and one of the variables will go away, or be eliminated.  In order for this to happen the coefficients of the variable in 1 of the equations must be the negative of the coefficient of the variable in the other equation.  So how can you get the coefficients of the variables to be the negative of each other?  Well, the y coefficients already have opposite signs (-1 and +7) so if you multiply the 1st equation by 7 you will be off to a good start.  

 

56x - 7y = 469

   x + 7y = 44 

 

If you add these 2 equations together the coefficient of the y variable will be 0 so you will have a single equation in a single variable that you can solve for x.  Once you get the value for x you can plug that value in to either of the 2 original equations and solve for y.  

 

If at any time during this process you end up with a false statement that is never true (like 0 = 5) then that means that there is no solution to the system.  If you end up with a tautology that is always true (like 0 = 0) then that means that there are infinitely many solutions to the system.