Question

Which BEST describes the system of equations?

y - 2x = 4
y + 2 = 2x
Consistent
Inconsistent
Consistent and Dependent
Consistent and independent

Answer 1

D) Consistent and Independent

Explanation:

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Answer 2

Inconsistent

Explanation:

Given system of equations.

A)
`y-2x=4`

B)
`y+2=2x`

We will solve the system of equations to check the solutions and tell whether the system is consistent or inconsistent

Rearranging equation A, to solve for
`y` in terms of
`x`

Adding both sides by
`2x`

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

`y=4+2x`

Substituting value of
`y` we got from A into equation B.

`4+2x+2=2x`

Simplifying.

`2x+6=2x`

Subtracting both sides by
`2x`

`2x-2x+6=2x-2x`

`6=0`

This is never true. So, we can say the system of equation has no solutions as the equations of the lines given are parallel.

Any system of equation with no solutions is termed as inconsistent.