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

OD

1 solution

Infinite

Answer 1

The system has unique solution.

Explanation:

Since the system has two unknow variables and two equations, we can resolve for one variable in the first equation and replace in the second equation.

We have the system

`x+y=4\\x-y=0`

We resolve for x in the first equation and obtain

`x=4-y`

Now, replace in the second equation the value of x,

`(4-y)-y=0\\4-2y=0\\y=2`

Now, replace the value of y in the expression of x:

`x=4-y=4-2=2`

Then the system has unique solution, (x,y)=(2,2)