Raphael graphed the system of equations shown.

Question

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)

Answer 1

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:

$\boxed{{\displaystyle (–2.2,–3)}}$.