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

Accepted Solution

Answer: Inconsistent.Step-by-step explanation: The  equation of the line in Slope-Intercept form is: [tex]y=mx+b[/tex] Where "m" is the slope and "b" is the y-intercept. Solve for "y" in each equation: Equation 1 [tex] x=-5-y\\\\y=-x-5[/tex] Equation 2 [tex]4+y=-x+3\\\\y=-x+3-4\\\\y=-x-1[/tex] You can notice that the slope of the Equation 1 is: [tex]m_1=-1[/tex] And the slope of the Equation 2 is: [tex]m_2=-1[/tex] Observe that [tex]m_1=m_2[/tex], 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".