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Raphael graphed the system of equations shown.

y = – 3
y = x – 0.8

A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?

(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)

1 answer

To find the intersection point of the given equations, we analyze the equations provided:

  1. The first equation is \( y = -3 \). This is a horizontal line where the value of \( y \) is always -3.

  2. The second equation is \( y = x - 0.8 \). This is a straight line with a slope of 1 and a y-intercept of -0.8.

To find the intersection of these two lines, we can set their y-values equal to each other:

\[ -3 = x - 0.8 \]

Now, solve for \( x \):

\[ x - 0.8 = -3 \] \[ x = -3 + 0.8 \] \[ x = -2.2 \]

Thus, the intersection point is approximately \((-2.2, -3)\).

Among the answer choices provided:

  • \((–3.2, –3)\)
  • \((–2.9, –3)\)
  • \((–2.2, –3)\)
  • \((–1.9, –3)\)

The best approximation for the solution to this system of equations is:

\(\boxed{(–2.2, –3)}\).