To find the solution of a system of equation graphed, it is the point where the two lines crosses with each other
for that we found the equation of the line for both of them using the points given
the slope for the orange line is 1/2
the slope for the green line is 1
the y-intercept for the orange line is 3
the y-intercept for the green line is 1
the equation for the orange line is
[tex]y=\frac{1}{2}x+3[/tex]
the equation for the green line is
[tex]y=x+1[/tex]
equal both of the equations
[tex]\begin{gathered} x+1=\frac{1}{2}x+3 \\ \frac{1}{2}x=2 \\ x=4 \end{gathered}[/tex]
using the equation to find the point where they cross
[tex]\begin{gathered} y=x+1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]
the solution of the system is (4,5)
