Question

determine the number of solutions to this system of linear equations (0, 1, ∞):
y = 7x + 8
-7x + y = -8
(1 point)
this system of linear equations has \boxed{} solution(s).

Explanation:

Step1: Rewrite the second equation

Let's rewrite the second equation \(-7x + y = -8\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept). We can solve for \(y\) by adding \(7x\) to both sides of the equation. So, \(y=7x - 8\).

Step2: Compare the two equations

The first equation is \(y = 7x+8\). For a linear equation \(y = mx + b\), the slope \(m\) of the first equation is \(m_1 = 7\) and the y - intercept \(b_1=8\). The slope of the second equation (after rewriting) is \(m_2 = 7\) and the y - intercept \(b_2=-8\).

Since the two lines have the same slope (\(m_1 = m_2=7\)) but different y - intercepts (\(b_1
eq b_2\)), the two lines are parallel. Parallel lines never intersect, so a system of linear equations representing two parallel lines has no solutions.

Answer:

\(0\)