Question

Classify the system of equations 2x=-3-y 4+y=-2x-2

intersecting
parallel
coincident

please hurry!

Answer 1

Second option: Parallel.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" in each equation:

Equation 1

`2x=-3-y \\\\2x+y=-3\\\\y=-2x-3`

Equation 2

`4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6`

You can notice that the slope of the Equation 1 is:

`m_1=-2`

And the slope of the Equation 2 is:

`m_2=-2`

Observe that
`m_1=m_2`, then you can conclude that the lines are: Parallel.

Answer 2

parallel

Explanation:

we have

2x=-3-y

isolate the variable y

y=-2x-3 ----> equation A

4+y=-2x-2

isolate the variable y

y=-2x-2-4

y=-2x-6 -----> equation B

Remember that

If two lines are parallel, then their slopes are the same

Line A and Line B have the same slope m=-2 and different y-intercept

therefore

The lines are parallel