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Shannon graphed the system of equations.

7x – 4y= –8
y = y equals StartFraction 3 over 4 EndFraction x minus 3.x – 3

A coordinate grid with 2 lines. The first line passes through (0, negative 3) and (negative 4, negative 6). The second line passes through (0, negative 2) and (negative 4, negative 6). The lines appear to cross at about negative 5 and between negative 6 and negative 8.
What is the closest approximate solution to the system of equations?

(–5, –7.2)
(–5, –6.8)
(–5, –6.2)
(–5, –5.9)

1 answer

To find the closest approximate solution to the system of equations based on the provided graph information, we can analyze the intersection point suggested by the coordinates provided.

The two equations are:

  1. \( 7x - 4y = -8 \)
  2. \( y = \frac{3}{4}x - 3 \)

According to the description, the lines intersect at a point around \( (-5, y) \).

Now, let's find the y-coordinate for \( x = -5 \) using the second equation, \( y = \frac{3}{4}(-5) - 3 \):

\[ y = \frac{3}{4}(-5) - 3 = -\frac{15}{4} - 3 = -\frac{15}{4} - \frac{12}{4} = -\frac{27}{4} \approx -6.75 \]

Given the options provided:

  • (–5, –7.2)
  • (–5, –6.8)
  • (–5, –6.2)
  • (–5, –5.9)

The closest approximate value to \(-6.75\) is \(-6.8\).

Therefore, the closest approximate solution to the system of equations is (–5, –6.8).