Question

how many solutions does the system of equations below have?
y = 4x - 8
y = \frac{-4}{5}x + \frac{6}{7}
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze slope of each line

The equations are in slope-intercept form $y=mx+b$, where $m$ is the slope.

• For $y=4x-8$, slope $m_1=4$
• For $y=\frac{-4}{5}x+\frac{6}{7}$, slope $m_2=\frac{-4}{5}$

Step2: Compare slopes

Since $m_1
eq m_2$, the lines intersect at exactly one point.

Answer:

one solution