Question

Which graph shows the solution to the system of linear equations?
y = 1/3 x
x + 3y = 6

Answer 1

The top right graph. I have circled this one in the attached figure to avoid confusion

Explanation:

The solution to the system of equations will be the value of x and y where both lines in the graph intersect

The two equations are
y = (1/3) x (1)

and

x + 3y = 6 (2)

Substitute y = (1/3) x in the second equation:
x + 3y = 6

=> x + 3 · (1/3)x = 6

=> x + x = 6

=> 2x = 6

=> x = 6/2 = 3

At x = 3, y = (1/3) ·3 = 1

So the solution is (3, 1)

The second graph(top right) has lines intersecting at x = 3, y = 1 i.e. point(3, 1)

So this graph represents the solution to the system of equations