Respuesta :

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So we need to find the two lines...y=mx+b where m is the slope and b is the y-intercept.

m=(dy/dx)=(7-6)/(3-1)=1/2 so

y=x/2+b, now I'll use (1,6) to solve for b

6=1/2+b, b=5 1/2=11/2 so

y1=(x+11)/2

now the other line...

m=(8-6)/(5-3)=2/2=1

y2=x+b, using point (3,6) we solve for b

6=3+b, b=3 so

y2=x+3

Since this is just two lines they will only intersect at a single point and when they do, y=y so we can say:

x+3=(x+11)/2

2x+6=x+11

x+6=11

x=5, now use either line to solve for the corresponding y value...

y2=x+3 becomes y=5+3=8 so the solution to this system is the point:

(5,8)

Answer:

(5, 8)

Step-by-step explanation:

Since, the linear equation defined by [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is,

[tex]y-y_1=\frac{x_2-x_1}{y_2-y_1}(x-x_1)[/tex]

Thus, the linear equation defined by points (1, 6) and (3, 7) is,

[tex]y-6=\frac{7-6}{3-1}(x-1)[/tex]

[tex]y-6=\frac{1}{2}(x-1)[/tex]

[tex]2y-12=x-1[/tex]

[tex]\implies x-2y=-11-----(1)[/tex]

Similarly, the linear equation is defined by points (3, 6) and (5, 8),

[tex]y-6=\frac{8-6}{5-3}(x-3)[/tex]

[tex]y-6=\frac{2}{2}(x-3)[/tex]

[tex]y-6=x-3[/tex]

[tex]\implies x-y=-3------(2)[/tex]

Equation (1) -  equation (2),

-y = -8

⇒ y = 8

From equation (1),

x-2(8)=-11

x-16=-11

x = - 11 + 16 = 5

Hence, point (5,8) represents the solution of this system of equations.

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