Question

What is the solution for the system of linear equations shown in the graph?

a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma negative 3 and another line that passes through the points 0 comma 2 and negative 1 comma 1

negative one half comma three halves
one half comma one half
three halves comma three halves
negative three halves comma one half

Answer 1

(a) (-1/2, 3/2)

Explanation:

You want the point of intersection of the line through points (0, 0) and (1, -3) and the line through points (0, 2) and (-1, 1).

Proportion

The first line passes through the origin, so represents a proportional relationship. The point (x, y) = (1, -3) on that line tells you the constant of proportionality is ...

k = y/x = -3/1 = -3

Any point on this line will have a y-value that is -3 times the x-value. Of the answer choices, the only one for which this is true is ...

(x, y) = (-1/2, 3/2) . . . . . choice A

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Additional comment

As we see, there is no need to write the equations of both lines and solve them as a system.

If you wanted to do that, you would find the slope of the second line is (2-1)/(0-(-1)) = 1. The y-intercept of that line is one of the given points, so its equation is y = x +2. Then the two equations together give you ...

-3x = y = x +2 ⇒ -4x = 2 ⇒ x = -1/2 . . . . . matches choice A

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