Question

determining when a sys
infinitely many solutions
▶ how many solutions does each system of
solving the system.
⑪ ( y = 3x + 12 )
( y = 3x )

Explanation:

Step1: Analyze the slopes and intercepts

The two equations are \( y = 3x + 12 \) and \( y = 3x \). Both are in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the first equation, \( m_1=3 \) and \( b_1 = 12 \). For the second equation, \( m_2=3 \) and \( b_2=0 \).

Step2: Determine the number of solutions

Since the slopes of the two lines are equal (\( m_1=m_2 = 3 \)) and the y - intercepts are different (\( b_1
eq b_2 \)), the two lines are parallel. Parallel lines in a plane do not intersect, so the system of equations has no solution.

Answer:

The system of equations has no solution.