We are given the following system of linear equations
[tex]\begin{gathered} x+y=-3\quad eq.1 \\ 4x+4y=-12\quad eq.2 \end{gathered}[/tex]
We are asked to solve the system of linear equations by graphing.
First, let us convert these equations into the slope-intercept form.
The slope-intercept form is given by
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
[tex]\begin{gathered} x+y=-3 \\ y=-x-3 \end{gathered}[/tex]
So, eq.1 has a slope of -1 and a y-intercept of -3
[tex]\begin{gathered} 4x+4y=-12 \\ 4y=-4x-12 \\ y=\frac{-4x-12}{4} \\ y=\frac{-4x}{4}-\frac{12}{4} \\ y=-x-3 \end{gathered}[/tex]
So, eq.2 has a slope of -1 and y-intercept of -3
This means that eq.1 and eq.2 are basically the same equations
This means that there is an infinite number of possible solutions.
The graph is given by
As you can see, both equations are superimposed on each other which means there infinite
