Question

question 5 (2 points)
(06.02)
what equation is solved by the graphed systems of equations?
options:
○ a 7x + 3 = x + 3
○ b 7x - 3 = x - 3
○ c 7x + 3 = x - 3
○ d 7x - 3 = x + 3

Explanation:

Step1: Find equations of two lines

First, take the steeper line. It passes through (0, 3) and (-1, -4). The slope \( m_1=\frac{-4 - 3}{-1 - 0}=\frac{-7}{-1} = 7\). Using slope - intercept form \(y = mx + b\), with \(b = 3\), equation is \(y=7x + 3\).

Second, take the other line. It passes through (0, -3) and (3, 0). The slope \(m_2=\frac{0-(-3)}{3 - 0}=\frac{3}{3}=1\). Using slope - intercept form \(y=mx + b\), with \(b=-3\), equation is \(y=x - 3\).

Step2: Find the equation solved by the system

The solution of the system of equations \(y = 7x+3\) and \(y=x - 3\) is found by setting them equal: \(7x + 3=x - 3\).

Answer:

c. \(7x + 3=x - 3\)