Question

For the graph shown, select the statement that best represents the given system of equations.

2y – x = 2
x – 2y = 8


a.
consistent and independent

b.
inconsistent

c.
coincident

d.
not enough information

Answer 1

Answer: Option 'b' is correct.

Explanation:

Since we have given that

2y-x=2

⇒2y=2+x

⇒2y-2=x--------------(1)

x-2y=8 --------------------(2)

Put the eq(1) in eq(2), we get that,

`x-2y=8\\\\2y-2-2y=8\\\\-2\\eq 8`

Here,

`a_1=-1,b_1=2,c_1=2\\\\a_2=1,b_2=-2,c_2=8`

Now,

`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)\\\\(-1)/(1)=(2)/(-2)=(2)/(8)\\\\-1= -1\\eq (1)/(4)`

So, it is the parallel line.

So, it is inconsistent.

Hence, Option 'b' is correct.

Answer 2

The best answer is inconsistent.