Question

Classify the system of equations x=-5-y 4+y=-x+3

Answer 1

Answer: Inconsistent.

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

`x=-5-y\\\\y=-x-5`

Equation 2

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

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

`m_1=-1`

And the slope of the Equation 2 is:

`m_2=-1`

Observe that
`m_1=m_2`, then you can conclude that the lines are parallel and the System of equations has No solution.

When there is no solution the classification of the system of equations is: "Inconsistent".