Question

87 POINTS

Classify the system
x + y = 3
2y = x

A. Inconsistent
B. consistent dependant
C. consistent independent

Answer 1

Option C. consistent independent

Explanation:

we know that

If a system has at least one solution, it is said to be consistent.

If a consistent system has exactly one solution, it is independent.

If a consistent system has an infinite number of solutions, it is dependent.

If a system has no solution, it is said to be inconsistent.

we have

`x+y=3` ----> equation A

`2y=x` ---->
`x=2y` ----> equation B

solve the system by substitution

substitute equation B in equation A

`2y+y=3`

solve for y

`3y=3`

`y=1`

Find the value of x

`x=2y` ---->
`x=2(1)=2`

The solution is the ordered pair (2,1)

The system has only one solution

therefore

The system is a consistent independent