In order to graph each equation, we need to choose two points that are solution of each equation.
To do so, we just need to choose a value of x and then calculate the corresponding value of x.
So for y = x + 6, we have:
[tex]\begin{gathered} x=0\colon \\ y=0+6=6 \\ \\ x=-1\colon \\ y=-1+6=5 \end{gathered}[/tex]Now, for y = -2x - 3, we have:
[tex]\begin{gathered} x=0\colon \\ y=0-3=-3 \\ \\ x=-1\colon \\ y=(-1)\cdot(-2)-3=2-3=-1_{} \end{gathered}[/tex]Graphing the points and the corresponding lines, we have:
To calculate the solution of the system of equations, we can equate both values of y from each equation:
[tex]\begin{gathered} x+6=-2x-3 \\ x+2x=-3-6 \\ 3x=-9 \\ x=-3 \\ \\ y=x+6 \\ y=-3+6 \\ y=3 \end{gathered}[/tex]So the solution is the ordered pair (-3, 3).
