We can solve the next system of equations
[tex]\begin{gathered} y=x-6 \\ x+2y=6 \end{gathered}[/tex]We can notice the graph of each equation will be a line because we have a first-degree equation.
The solution of the this system is where the lines intercept each other, we will graph some points in other to help us to see the graph of the equation
First equation
x y
0 -6
1 -5
2 -4
3 -3
4 -2
5 -1
6 0
In the case of the second equation, we need to clear y
[tex]y=-\frac{x}{2}+3[/tex]x y
0 3
1 5/2
2 2
3 3/2
4 1
5 1/2
6 0
If we graph these points we will obtain the next graph
as we can see the solution of the system is
x=6, y=0
