Question

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)

Answer 1

Substitute y = (3/4)x − 3 into 7x − 4y = −8:

7x − 4((3/4)x − 3) = −8
7x − 3x + 12 = −8
4x = −20 → x = −5

y = (3/4)(−5) − 3 = −15/4 − 3 = −27/4 = −6.75

Rounded to one decimal, the intersection is (−5, −6.8). So choose (−5, −6.8).