Question

Classify the system of equations. 3x = -2- y 4+ y = -3x+1 Click on the correct answer. intersecting parallel coincident

Answer 1

Explanation:

rearrange the equations first

y=-3x-2---eq(1)

y=-3x+1-4

y=-3x-3---eq(2)

In first eq slope is -3x and y-intercept is -2

In second equation, the slope is -3x and y-intercept is -3

the slopes are the same in both equations but the y-intercepts are different

so the lines are parallel. The system is inconsistent

Answer 2

For this case we have the following system of equations:

`3x = -2-y\\4 + y = -3x + 1`

By clearing "y" from both equations we have:

Equation 1:

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

Equation 2:

`y = -3x + 1-4\\y = -3x-3`

It is observed that the slopes of both equations are equal. Recall that the equation of a line in the slope-intersection form is given by:

`y = mx + b`

Where "m" is the slope.

If the slopes are equal, then the lines are parallel.

Answer:

Parallel