Question

how many solutions does the system of equations below have?
y = 8x + 10
y = 8x + 10
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the equations

The two equations are \( y = 8x + 10 \) and \( y = 8x + 10 \). They are identical.

Step2: Determine the number of solutions

For a system of linear equations \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \), if \( m_1=m_2 \) and \( b_1 = b_2 \), the lines are coincident (they overlap completely). So every point on the line is a solution, meaning there are infinitely many solutions.

Answer:

infinitely many solutions