Question

how many solutions does the system of equations below have?
$y = 8x + \frac{9}{8}$
$y = 8x + \frac{9}{8}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the equations

The two equations given are \( y = 8x+\frac{9}{8} \) and \( y = 8x+\frac{9}{8} \). They are identical linear equations.

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 lie on top of each other). When two lines are coincident, every point on one line is also on the other line, so there are infinitely many solutions.

Answer:

infinitely many solutions