Answer:
no solutions: the y-intercept must be changed
infinite solutions: the equation must describe the same line
Step-by-step explanation:
No Solutions
For the system of equations to have no solutions, the equations must describe parallel lines. The lines will have the same slope (m), but will have different y-intercepts (b).
The second equation could be ...
y = mx +b1 . . . . . where b1 ≠ b
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Infinitely Many Solutions
The two equations of the system must describe the same line. The second equation must reduce to exactly the same equation as the one given: y = mx +b. It could be this equation multiplied by a constant, for example:
ky = mkx +kb . . . . . equation multiplied by k
Or, it could be rearranged:
mx -y +b = 0 . . . . . general form
mx -y = -b . . . . . . . .standard form
y -b = mx . . . . . . . . point-slope form; line with slope m through point (0, b)
