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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

User Mziccard
by
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1 Answer

4 votes

Answer:

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)

User Ramya Ramachandran
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