A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below.

(2, 0)

Step-by-step explanation:

First we need to get the equation of the line passing through the points (3, 1) and (–5, –7)

Equation of a line is y = mx+c

m is the slope

m = y2-y1/x2-x1

m = -7-1/-5-3

m = -8/-8

m = 1

Substitute m = 1 and the point (3, 1) into the equation y = mx+c and get c;

1 = 1(3) + c

1 = 3 + c

c = 1-3

c = -2

The required equation is y = x - 2

We are to look for the coordinate point (x,y) for which both lines intersects, then both equations will be equal as shown;

0.5x - 1 = x - 2

0.5x - x = -2+1

-0.5x = -1

x = -1/-0.5

x = 2

Substitute x = 2 into y = x - 2

y = 2-2

y = 0

Hence the the coordinate point is (2, 0)

x = 3 ± √(5+y)