Final answer:
The solution to the system of equations is the point (2, 0).
Step-by-step explanation:
To find the solution to the system of linear equations, we need to find the point where the two lines intersect. The first line, y = 0.5x - 1, has a slope of 0.5 and a y-intercept of -1. The second line passes through the points (3, 1) and (-5, -7). We can find the slope of the second line using the formula m = (y2 - y1) / (x2 - x1), which gives us a slope of m = (-7 - 1) / (-5 - 3) = -8 / -8 = 1. Now we have the equations y = 0.5x - 1 and y = x + b. To find b, we can substitute the coordinates of one of the points (3, 1) into the equation and solve for b: 1 = 3 + b, b = -2. So the equation of the second line is y = x - 2. To find the point of intersection, we can set the two equations equal to each other: 0.5x - 1 = x - 2. Solving for x gives us x = 2. Substituting x = 2 into one of the equations gives us y = 0.5(2) - 1 = 0. So the solution to the system of equations is the point (2, 0).