Answer:
The solution to the system of equations is x = 4 and y = 2.
Step-by-step explanation:
From statement we know that the first line is [tex]y = 0.5\cdot x[/tex]. The second line is determined by knowing two distinct points and solving the resulting system of equations by definition of the equation of the line:
[tex](x_{1},y_{1}) = (3,1)[/tex] and [tex](x_{2}, y_{2}) =(-5,-7)[/tex]
[tex]3\cdot m + b = 1[/tex] (1)
[tex]-5\cdot m + b = -7[/tex] (2)
The solution of the system of equations is:
[tex]m = 1[/tex], [tex]b = -2[/tex]
The second line is represented by [tex]y = x-2[/tex]. And the resulting system of equations is:
[tex]0.5\cdot x -y = 0[/tex] (3)
[tex]x-y = 2[/tex] (4)
The soltuion to the system of equations is:
[tex]x = 4[/tex], [tex]y = 2[/tex]
The solution to the system of equations is x = 4 and y = 2.
