substitution Method 6x-6y=24, x-y=4

Question

Give your ordered pair
solution in solution set notation.
If the system
has dependent e
quati
ons
, give solution
set in set
-
builder notation
.

Answer 1

These two equations are dependent. You can tell because one is a multiple of the other:

 

6(x - y = 4) --> 6x - 6y = 24

 

 

You can also tell by substitution. Solve the second equation for x, then plug that into the first equation and solve:

 

x = y + 4

 

6x - 6y = 24

6(y + 4) - 6y = 24

6y + 24 - 6y = 24

24 = 24

 

That equation is always true (24 is always equal to 24), so you've got an infinite number of solutions. That means the equations are dependent.

 

 

So, in set-builder notation, your solution set is:

 

{(x, y) | x - y = 4},

 

which means any pair of numbers x and y that fulfills the equation x - y = 4.