Consider the pair of linear equations below.
Part A: What is the relationship, if any, between 12 and 6?
Part B: Do the two equations have one solution, no solution, or infinitely many solution? Explain.
Part C: How can you verify your answers to Part A and B by solving algebraically?
math - Henry, Wednesday, April 3, 2013 at 9:29pm
Eq1: 4x + 6y = 12.
m1 = -A/B = -4/6 = -2/3.
Y-int. = C/B = 12/6 = 2.
Eq2: 2x + 3y = 6.
m2 = -2/3.
Y-int. = 6/3 = 2.
Since the slopes and Y-intercepts are both equal, the Eqs represent the same line. Therefore, we have an infinite number of solutions.
Multiply both sides of Eq2 by 2 and compare the Eqs.
If the slopes were not equal, there will be one solution.
If the slopes were equal with unequal Y-intercepts, we'll have no solutions.
In this case, we have two parallel lines.