How do you solve systems of equations by elimination

Question

The problem is -16+20x-8y=0 and 36=-18y-22x

 

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 cancel out, or be eliminated.  In order for this to occur, the coefficients of the variable in the 2 equations must be the negative of each other.  The first step is to write the 2 equations in the standard form Ax + By = C 

 

 20x - 8y   = 16

-22x - 18y = 36  

 

The next step is to simplify each equation by dividing out common factors.  While not strictly necessary to solve the problem, this will make the numbers smaller so later calculations will be easier.  We can divide the 1st equation by 4 and the second equation by 2 to obtain 

 

   5x - 2y  = 4

-11x - 9y = 18

 

Next we pick which variable to eliminate, whichever is easier.  I will choose the x's since they already have opposite signs.  If we multiply the 1st equation by 11 and the 2nd equation by 5 we obtain 

 

 55x - 22y = 44

-55x - 45y = 90

 

Now we add the 2 equations together to eliminate x, and solve the resulting equation for y 

 

-67y = 134   ==>   y = 134/(-67) = -2  

 

Now plug back in to one of the original equations to solve for x 

 

-16 + 20x - 8(-2) = 0   ==>  20x = 0   ==>  x = 0

 

The last step is to check the solution x = 0 and y = -2 in the original equations  

 

-16 + 20(0) - 8(-2) = 16 + 16 = 0.  Check

36 = -18(-2) - 22(0) = 36.  Check