Question

use a graph to determine the number of solutions of th
y = 2x + 1

y = 2x + 5

one solution

no solution

infinitely many solutions

Explanation:

Step1: Analyze the equations' slopes

The two equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y = 2x+1\), the slope \(m_1 = 2\), and for \(y = 2x + 5\), the slope \(m_2=2\).

Step2: Analyze the y - intercepts

The y - intercept of \(y = 2x + 1\) is \(b_1=1\), and the y - intercept of \(y = 2x+5\) is \(b_2 = 5\). Since the slopes are equal (\(m_1=m_2\)) and the y - intercepts are different (\(b_1
eq b_2\)), the two lines are parallel. Parallel lines never intersect, so the system of equations has no solution.

Answer:

no solution