Hi! I need help with this question. Thanks!
Directions: Try to find the number of solutions for the following system of equations then determine if it is Dependent, Inconsistent or Consistent.
-3x-2y=6
x=-2-2/3y
The first step is to convert one equation into the same form as the other. Most of the time, we would convert the second to the form of the first, i.e.
x=-2-(2/3)y (parentheses added according to rules of BEMPAS, or PEDMAS.
x+2=-(2/3)y
Multiply by 3 on bothe sides
3x+6=-2y
6=-2y-3x
6=-3x-2y
which is identical to the first equation.
For a system of two linear equations, the possible cases are:
1. no solution (two lines are parallel and distinct) [inconsistent]
2. exactly one solution (two lines intersect at one point) [consistent]
3. an infinite number of solutions (two lines are parallel and coincident, so any point on one line lies on the other as well) [dependent, because given any value of x, we can find y]