Inactive Tutor answered • 06/09/13
To use substitution, you want to use one equation to define one variable in terms of the other. Then you substitute that expression into the other equation and begin solving. In this problem, they were kind enough to give you equation 1 as y in terms of x. So we'll use that to plug in for y in equation 2. Let's go!
Eqn 1: y = 4x + 1 --> substitute into Eqn 2: 8x-2y = -2
8x - 2(4x+1) = -2
Solve for x: 8x - 8x -2 = -2 --> -2 = -2 Huh?! Yep, it doesn't matter what x is, y will always be equal. They are the same line! In other words, this set of equations as infinitely many solutions (all x). Let's look back at the question. You'd expect something odd because it asks if the system is consistent (at least 1 solution), inconsistent (no solution), or dependent (infinite solutions).
Well, it's consistent dependent since the system has infinitely many solutions which is also ≥ 1 solution.
CHECK: Well if you hadn't been told to do substitution, notice that if you divided both sides of equation 2 by 2, you get equation 1. √
Note: Had this system resulted in x=value after substitution, you would have then plugged that value of x back into equation 1 to get the value of y. In other words, this would have been the case that the two lines intersected in a point (x,y) or consistent independent.
