Solve using the elimination method.

Question

x+y=12

-x+5y=12

 

 

A) The solution of the system is __.(Type an order pair)

B) There are infinitely many solutions.

C) There are no solution.

Answer 1

The elimination method involves adding or subtracting the two equations, or some multiple(s) of the equations, in a way that allows one of the variables to cancel out.  That leaves another equation with just one variable, which can then be solved.

 

x + y = 12
-x + 5y = 12

 

Notice that there's an x in one equation and a -x in the other.  If you add the two together, the x's will cancel:

 

x + y + -x + 5y = 12 + 12

 

Simplify:

6y = 24

 

Solve:

y = 4

 

And since x + y = 12, x must be 8.

 

So the answer is A, with the ordered pair being (8, 4)