Question

The coordinates below represent two linear equations. How many solutions does this system of equations have?

Answer 1

Use the points to find the equations of both your lines.
By using the formula for finding slope where: m = (y2-y1) / (x2-x1)
Your first equation is             y = -2x+4
Your second equation is        y = -2x+7
Normally you want to set these equal to each other and see where they are equal... however, as you can clearly see, these two equations are parallel. Parallel equations don't intersect, which would mean your answer is A, no solutions.