Question

Select the correct point

One linear equation is defined by points (1,6) and (3, 7), while the other is defined by points (3,6) and (5,8). Which point represents the solution of
this system of equations?

Answer 1

Explanation:

o find the solution of a system of linear equations, we can find the point where the two lines intersect. The point of intersection represents the solution to the system of equations.

The first linear equation can be determined by finding its slope and y-intercept using the given points:

m = (7 - 6) / (3 - 1) = 1

b = 6 - m * 1 = 6 - 1 * 1 = 5

y = mx + b

y = x + 5

The second linear equation can be found similarly:

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

b = 6 - m * 3 = 6 - 1 * 3 = 3

y = mx + b

y = x + 3

Since the two lines have the same slope, they are coincident and represent the same line. The solution to the system of equations is therefore any point on this line, but since we were asked for a specific point, we can choose (3,6) as the solution.