Question

Given the following system of equations, identify the type of system.

x + y = 6
y = 3 - x


consistent
inconsistent
equivalent

Answer 1

The system of equations is inconsistent

Explanation:

we have

`x+y=6`

`y=6-x` -----> equation A

`y=3-x` -----> equation B

equation A and equation B has the same slope

so

The lines are parallel

The system has no solution

therefore

The system of equations is inconsistent

Answer 2

Equations are inconsistent.

Explanation:

Given : x + y = 6

y = 3 - x.

To find : Identify the type of system.

Solution : We have given that

x + y = 6 →→→→→→→( equation 1).

y = 3 - x →→→→→→→( equation 2).

Plugging the values of y = 3 - x from equation (2) in equation (1).

x + (3 - x ) = 6

x + 3 - x = 6.

3 = 6

It has no solution , these lines are parallel.

Therefore, Equations are inconsistent.