Question

$y = 5x$
$y = 5x + 20$
how many solutions does this system of equations have?
no solutions, because there are no ordered pairs that make both equations true.
infinitely many solutions, because $y$ can be any value.
one solution, because $x$ must be 0 and $y$ must be 20.

Explanation:

Step1: Compare slopes and intercepts

The equations are in $y=mx+b$ form. For $y=5x$, slope $m_1=5$, y-intercept $b_1=0$. For $y=5x+20$, slope $m_2=5$, y-intercept $b_2=20$.

Step2: Analyze parallel lines

Equal slopes ($m_1=m_2$) mean lines are parallel. Different intercepts ($b_1
eq b_2$) mean lines never intersect.

Step3: Determine number of solutions

Parallel, non-intersecting lines have no shared ordered pairs.

Answer:

No solutions, because there are no ordered pairs that make both equations true.