Question

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

Answer 1

Answer: Inconsistent.

Step-by-step 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

$-\frac{1}{2}x=3-y\\\\y=\frac{1}{2}x+3$

Equation 2

$-7+y=\frac{1}{2}x-2\\\\y=\frac{1}{2}x-2+7\\\\y=\frac{1}{2}x+5$

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

$m_1=\frac{1}{2}$

And the slope of the Equation 2 is:

$m_2=\frac{1}{2}$

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".