Question

how many solutions does the system have?\

$$\begin{cases}y = -7x + 8\\\\y = -7x - 8\\end{cases}$$

choose 1 answer:\\(\boldsymbol{\text{a}}\\) exactly one solution\\(\boldsymbol{\text{b}}\\) no solutions\\(\boldsymbol{\text{c}}\\) infinitely many solutions

Explanation:

Step1: Analyze the slopes of the two lines

The equations are in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the first equation \(y=-7x + 8\), the slope \(m_1=-7\). For the second equation \(y=-7x-8\), the slope \(m_2=-7\). Since \(m_1 = m_2\), the two lines are parallel.

Step2: Analyze the y - intercepts

The y - intercept of the first line \(b_1 = 8\) and the y - intercept of the second line \(b_2=-8\). Since \(b_1
eq b_2\), the two parallel lines do not coincide. Parallel lines that do not coincide have no intersection points, which means the system of equations has no solutions.

Answer:

B. No solutions