Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 4
x - y = 0

Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
x + y = 4
x - y = 0

anonymous · Answer

1. contains one point (x=2, y=2) 

2. contains one point (x=2, y= -3) 

3.empty set;equations have the same gradient, they are parallel 

4. contains one point (x=2 , y=0) 

5. infinite solutions; both equations are the same. 

6. C (-1,5) 

7. C (-2,-3)

anonymous · Answer

add the two equations together and get 2x=6 and therefore x=3

imstuck · Answer

No that's not correct, @thomas.charles27.  You have to solve these simultaneously to see what the x and the y are.

imstuck · Answer

x+y=4
x-y=0
For the first one, y = 4-x and for the second one -y=-x+0 or y = x.  So sub in x for y in one of the eqautions and you will get x=4-x.  Add x to both sides to get 2x=4 so x = 2.  Then sub 2 in for x in one of the equations, andd you will get 2+y=4 and y = 2.  So the solution set is x=2, y=2.