infinitely many solutions

Question

infinitely many solutions in a system of equations with 5x-2y=8 in y = mx + b form please

Answer 1

Hi Katie! Infinitely many solutions happens when we graph the same line on the coordinate plane. Since the lines are the same, they will lay right on top of each other. This gives infinitely many solutions. All you need to do is write the equation that you were given in slope-intercept form. 5x - 2y = 8 can be written as -2y = -5x + 8. We can divide both sides by -2 and get y = 5/2x - 4. This is our answer, because it is exactly the same line as 5x - 2y = 8, just written in a different form.

Answer 2

y = 5/2 x - 4 is the line solved for y and in mx + b form. All lines with the same slope will be parallel and not intersect this line (no solution for shared x and y). That is, all lines that look like y = 5/2 x + b where b ≠ 4