math
posted by Jayson Angole on .
Consider the pair of linear equations below.
4x+6y=12
2x+3y=6
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?

Eq1: 4x + 6y = 12.
m1 = A/B = 4/6 = 2/3.
Yint. = C/B = 12/6 = 2.
Eq2: 2x + 3y = 6.
m2 = 2/3.
Yint. = 6/3 = 2.
Since the slopes and Yintercepts 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 Yintercepts, we'll have no solutions.
In this case, we have two parallel lines.