Question

Classify the system of equations -1/2x=3-y -7+y=1/2x-2

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

`-(1)/(2)x=3-y\\\\y=(1)/(2)x+3`

Equation 2

`-7+y=(1)/(2)x-2\\\\y=(1)/(2)x-2+7\\\\y=(1)/(2)x+5`

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

`m_1=(1)/(2)`

And the slope of the Equation 2 is:

`m_2=(1)/(2)`

Observev 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".