Question

$y = 2x - 3$
$y = 2x + 1$
how many solutions does this system of equations have?
one solution
no solution
infinitely many solutions

Explanation:

Step1: Compare slopes of the lines

Both equations are in slope-intercept form $y=mx+b$, where $m$ is the slope. For $y=2x-3$ and $y=2x+1$, the slope $m=2$ for both.

Step2: Compare y-intercepts

The y-intercept $b$ for $y=2x-3$ is $-3$, and for $y=2x+1$ it is $1$. They are different.

Step3: Determine number of solutions

Parallel lines (same slope, different intercepts) never intersect, so no $(x,y)$ satisfies both equations.

Answer:

no solution