Respuesta :
Answer:
(3,1) is the correct answer.
Step-by-step explanation:
It is given that first line passes through (0,4) and (3,1)
Let the two points be at coordinates:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
[tex]x_1=0,\\y_1= 4,\\x_2=3,\\y_2= 1[/tex]
Equation of a line using two coordinates is given as:
[tex]y = mx+c[/tex]
[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{1-4}{3-0} = \dfrac{-3}{3} =-1[/tex]
Put x = 0, y = 4
[tex]4 = 0 +c\\\Rightarrow c = 4[/tex]
So, first equation is: [tex]y = -x +4 ...... (1)[/tex]
It is given that second line passes through (0,-2) and (3,1)
Let the two points be at coordinates:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
[tex]x_1=0,\\y_1= -2,\\x_2=3,\\y_2= 1[/tex]
Equation of a line using two coordinates is given as:
[tex]y = mx+c[/tex]
[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{1-(-2)}{3-0} = \dfrac{3}{3} =1[/tex]
Put x = 0, y = -2
[tex]-2 = 0 +c\\\Rightarrow c = -2[/tex]
So, second equation is: [tex]y = x -2 ...... (2)[/tex]
Solving equations (1) and (2) using substitution:
Adding Equation (1) and (2):
[tex]2y = 4-2\\\Rightarrow y =1[/tex]
Putting value y = 1 in equation (1):
[tex]1 = -x+4\\\Rightarrow x =3[/tex]
So, the solution for the system of equations is: (3,1)