The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below.

On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5).

Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1?
(–0.3, 2.1)
(–0.3, –2.1)
(0.9, –1.8)
(0.9, 1.8)
46 points quickly

  (–0.3, 2.1)

Step-by-step explanation:

The graph shows you the solutions for any pair of lines you care about. So, the problem is to figure out which are the lines you care about.

The graph shows you the lines all differ in their y-intercepts. This means you can identify the y-intercepts of the equations of interest, and you will know which lines to look at.

The y-intercept is found by setting x=0 and solving for y:

x +5y = 10

  0 + 5y = 10

  y = 10/5 = 2

3x +y = 1

  3·0 +y = 1

  y = 1

The two lines of interest are the ones that have y-intercepts of 2 (pink) and 1 (blue). They intersect in the 2nd quadrant. Only one answer choice can apply:

  (–0.3, 2.1)