Do we have to find the value of x separately by elimination and y separately by elimination in a question for solving by elimination?

Question

In solving a linear equations in two variables for x and y, if question is set for solving by elimination, do we have to find the value of x separately by elimination and y separately by elimination?

Answer 1

You will find that many tutors, teachers, and textbooks say that they solve "by elimination" when they actually solve for one variable by elimination then solve for the second variable by substitution (see other tutor's posts).

 

However, you may solve for the second variable by elimination rather easily in many problems; so why not do it?

 

Here is an actual problem posted on the WyzAnt Answers site:

x+2y=0

x+y=-1

To solve by elimination, we make the coefficient of one variable the same (or opposite) so we may "eliminate" it by adding (or subtracting) and solve for the other variable.

  x +2y = 0
  x + y =-1

------------- [elimination; subtract equations]

        y  = 1

 

Now, while it is pretty easy to substitute 1 for y in the second equation (or the first equation for that matter) then solve for x, you may also write (or just continue using another line):

  x + y = -1     [second equation]

        y =  1       [previous solution]

--------------   [elimination; subtract equations]

  x       =  -2

 

You mentioned solving "separately."  You could do that, but if you have already solved for one of the variables, use that information to solve for the other variable (either by elimination or by substitution).

 

My experience is that using elimination to solve for the second variable is often easier and quicker; it depends on the coefficients of the variables given in the original equations.

Answer 2

Nope! You just need to solve for one of the variables.  Then you can plug that value into either of the original equations and solve for the other variable.  

 

So, if we were given 

x + 2y = 7

2x + 3y = 5

 

we could eliminate x by multiplying the first equation by two and subtracting the second equation from it.

 

2x + 4y = 14

2x + 3y = 5

____________

        y = 9

 

 

Then just plug that back into either equation

 

x + 2(9) = 7

x + 18 = 7

x = -11

 

If we had plugged y into the other equation, we would have gotten the same thing.

 

2x + 3(9) = 5

2x + 27 = 5

2x = -22

x = -11

 

Both give the same x, and our solution is (-11,9).

Answer 3

No. You would use elimination to eliminate one of the variables and solve for the 2nd variable. Once you find that value, plug it into either equation and solve for the remaining value. But be sure to go back and check your solution in both equations.