Question

Determine the solution to the system of linear equations graphically if the system is dependent or inconsistent state

Answer 1

In order to solve the system graphically, we need to graph both equations from the system.

To do so, we can find two ordered pairs that are solutions for each equation.

Choosing a value of x and calculating the corresponding value of y, we have:

`\begin{gathered} 5x+y=-21 \\ x=-4\colon \\ -20+y=-21 \\ y=-21+20=-1 \\ x=-5\colon \\ -25+y=-21 \\ y=-21+25=4 \\ \\ 2x+2y=-2 \\ x=0\colon \\ 2y=-2\to y=-1 \\ x=-1\colon \\ -2+2y=-2\to y=0 \end{gathered}`

So for the first equation we have the points (-4, -1) and (-5, 4), and for the second equation we have (0, -1) and (-1, 0).

Graphing these points and the corresponding lines, we have:

Since the lines intersect at just one point, so the system is independent.