Question

determine the number of solutions for the following system of equations.
$y = 5x + 7$
$y = 5x - 10$
one solution
two solutions
infinitely many solutions
no solution

Explanation:

Step1: Compare slopes of lines

Both equations are in slope-intercept form $y=mx+b$, where $m$ is the slope. For $y=5x+7$ and $y=5x-10$, the slope $m=5$ for both.

Step2: Compare y-intercepts

The y-intercept $b$ for the first line is $7$, and for the second line is $-10$. These are not equal.

Step3: Analyze solution count

Parallel lines (equal slopes, different intercepts) never intersect, so there are no points $(x,y)$ that satisfy both equations.

Answer:

No solution