Question

For the following set of equations, determine (a) if the system is a linear system of equations, (b) the number of solutions to the system, (c) if the system is consistent or inconsistent, and (d) if the system is independent or dependent.y + x = 42y − 2x = 8

Answer 1

Given the system of equations:

$\begin{gathered} y+x=4\rightarrow(1) \\ 2y-2x=8\rightarrow(2) \end{gathered}$

a) The given system has the equations of lines, so it will be a linear system

b) We will write the equations in slope-intercept from to compare them

From (1): y = -x + 4

From (2): y = x + 4

The slope of the first equation = -1, and the slope of the second equation = 1

so, the given system of consistent independent system

the system has only one solution

c) the system will be consistent

d) the system will be independent